Radio wave receiving apparatus, radio wave receiving circuit and radio wave timepiece

[0001] This application is based upon and claims the benefit of priority from the prior Japanese Patent Application No. 2005-217469, filed on Jury 27, 2005, and 2005-345640, filed on Nov. 30, 2005 and the entire contents of which are incorporated herein by reference.

[0002] 1. Field of the Invention

[0003] The present invention relates to, for example, a radio wave receiving apparatus for receiving standard radio waves, a radio wave receiving circuit and a radio wave timepiece.

[0004] 2. Description of the Prior Art

[0005] Recently, in various countries, for example, Germany, England, Switzerland, Japan and the like, time data, that is, standard radio waves containing a time code are being transmitted. In Japan, long wave standard radio waves of 40 kHz and 60 kHz with time codes which are amplitude modulated, using the standard time format, are sent from two transmitting stations (Fukushima and Saga). This time codes are sent with the frame the cycle of which is 60 seconds, for every occasion when the place of minute of the exact time is updated, that is, for every 1 minute.

[0006] In recent years, so-called radio wave timepieces have been commercially available, in which standard radio waves containing the above-described time-codes are received to adjust the current time. Radio wave timepieces receive standard radio waves through a built-in antenna and perform amplification, detection and the like of the received signal, thereby to decode the time code and to adjust the current time. Radio wave timepieces capable of receiving a plurality of standard radio waves different in frequency, which are so-called multiband radio wave timepieces are known.

[0007] The radio-wave receiving apparatuses used in multiband radio wave timepieces are mainly based on a super-heterodyne system in which a received signal is synthesized with a local oscillating signal having a predetermined frequency to convert into an intermediate-frequency signal (IF signal), and the intermediate-frequency signal is referenced to perform detection. In this case, it is necessary to provide a local oscillating signal having a frequency, depending on the frequency of the standard radio wave to be received.

[0008] Therefore, the constitutions therefor are known, namely, (1) a constitution in which a plurality of local oscillating circuits are provided for outputting a local oscillating signal corresponding to the frequency of the standard radio wave to be received, (2) a constitution in which one unit of a local oscillating circuit is provided and the oscillatory frequency of the local oscillating circuit is changed over by turning a received frequency selecting switch ON/OFF, and (3) a constitution in which a local oscillating circuit is used also as an oscillating circuit for measuring time and the frequency is divided by the frequency-dividing ratio corresponding to the frequency of the standard radio wave which receives a reference frequency signal of 32.768 kHz output from the oscillating circuit for timepieces, to give a local oscillating signal.

[0009] However, the above-described conventional multiband radio wave receiving apparatus has the following problems. Namely, in the case of (1) where a plurality of oscillating circuits are provided corresponding to the frequencies of standard radio waves to be received, a radio wave receiving apparatus is inevitably provided with a larger sized circuit, thereby resulting in an increased cost and a restricted frequency of standard radio waves that can be received, which is a problem. Further, in the case of (2) where a local oscillating circuit is provided, the local oscillating circuit is constituted with, for example, a PLL (Phase Locked Loop) circuit having a VCO (Voltage Controlled Oscillator) and the PLL circuit requires a certain time from power-on to a stable operation and an oscillatory frequency output from the VCO may be rendered unstable, depending on setting of the reference frequency, which is also a problem.

[0010] In addition, in the case of (3) where the reference frequency signal for measuring time is frequency-divided to give a local oscillating signal, the frequency-divided signal is not in perfect coincident with the frequency necessary for converting the frequency of a received signal into an intermediate frequency, thereby to make it impossible to perform an accurate detection due to a difference in frequency, which is also a problem.

[0011] In the radio-wave receiving apparatus according to the invention, a signal received by a receiving antenna is amplified by an RF amplification circuit and the amplified received signal is input into a multi-stage frequency conversion circuit including a plurality of basic circuits connected in series. The multi-stage frequency conversion circuit converts the frequency of the received signal from the antenna into frequencies based on signals input from the frequency divider circuit sequentially, thereby to output a signal which is obtained by conversions into gradually lower frequencies. Detection is performed by a detection circuit on the basis of the signal. Thereby, a radio-wave receiving apparatus which requires no local oscillating circuit nor a PLL circuit and is also stable in operation and high in accuracy is realized.

[0012] The present invention will become more fully understood from the detailed description given hereinafter and the accompanying drawings which are given by way of illustration only, and thus are not intended as a definition of the limits of the scope of the invention, and wherein:

[0013] FIG. 1 is a block diagram of a radio wave timepiece of an embodiment in the present invention;

[0014] FIG. 2 is a block diagram of a radio wave receiving apparatus of the present invention;

[0015] FIG. 3 is a block diagram of a basic circuit of the present invention;

[0016] FIG. 4 is a block diagram of a detection circuit of the present invention;

[0017] FIG. 5A to FIG. 5D are views illustrating an image of a frequency spectrum in explaining an operation of receiving the standard radio wave of 40 kHz in the present invention;

[0018] FIG. 6 is a view illustrating a case where an operation of receiving the standard radio wave of 40 kHz is regarded as an extremely narrow band of a BPF (band pass filter) in the present invention;

[0019] FIG. 7A to FIG. 7D are views illustrating an image of a frequency spectrum in explaining an operation of receiving the standard radio wave of 77.5 kHz in the present invention;

[0020] FIG. 8A to FIG. 8B are views illustrating an image of a frequency spectrum in explaining an operation of receiving the standard radio wave of 77.5 kHz in the present invention;

[0021] FIG. 9 is a view illustrating a case where an operation of receiving the standard radio wave of 77.5 kHz is regarded as an extremely narrow band of a BPF in the present invention;

[0022] FIG. 10 is a list of frequency-divided signals and signals subjected to frequency conversion (multiplication synthesis) in a case of receiving standard radio waves of individual frequencies in the present invention;

[0023] FIG. 11A is a block diagram of a basic circuit of Embodiment 1 in the present invention;

[0024] FIG. 11B is a block diagram of-another basic circuit of Embodiment 1 in the present invention;

[0025] FIG. 12 is a block diagram of-a radio wave receiving apparatus of Embodiment 2 in the present invention;

[0026] FIG. 13A is a block diagram of a basic circuit of Embodiment 2 in the present invention;

[0027] FIG. 13B is a table showing the relationship between the use/non-use of a basic circuit 624B given in FIG. 13A and the connected state of switches SW2 and SW3;

[0028] FIG. 14A is a block diagram of a basic circuit of Embodiment 3 in the present invention;

[0029] FIG. 14B is a table showing the relationship between the use/non-use of a basic circuit 624C given in FIG. 14A and the connected state of switches SW5 and SW3;

[0030] FIG. 15 is a block diagram of a radio wave receiving apparatus of Embodiment 4 in the present invention;

[0031] FIG. 16 is a block diagram of a radio wave receiving apparatus of an exemplary modification in the present invention;

[0032] FIG. 17A is a view of explaining an image signal;

[0033] FIG. 17B is a view of explaining an image signal;

[0034] FIG. 18 is a block diagram of a basic circuit of Embodiment 5 in the present invention;

[0035] FIG. 19 is a block diagram of a phase-shift circuit of Embodiment 5 in the present invention;

[0036] FIG. 20A is a view of explaining a principle of removing an image signal of Embodiment 5 in the present invention;

[0037] FIG. 20B is a view of explaining a principle of removing an image signal of Embodiment 5 in the present invention;

[0038] FIG. 21 is a block diagram of a radio wave receiving apparatus of an exemplary modification in the present invention;

[0039] FIG. 22 is a block diagram of a multi-stage frequency conversion circuit of an exemplary modification in the present invention;

[0040] FIG. 23A is a conceptual view illustrating the phase relationship between two signals generated by frequency conversion at the first stage in the exemplary modification of the present invention;

[0041] FIG. 23B is a conceptual view illustrating the relationship of frequencies between two signals generated by frequency conversion at the first stage in the exemplary modification of the present invention;

[0042] FIG. 24A and FIG. 24B are conceptual views illustrating the phase relationship between two signals generated from frequency conversion at the second stage in the exemplary modification of the present invention;

[0043] FIG. 25 is a conceptual view illustrating the relationship of frequencies between two signals generated by frequency conversion at the second stage in the exemplary modification of the present invention; and

[0044] FIG. 26 is a table illustrating operational contents of individual adders-subtractors in the multi-stage frequency conversion circuit given in FIG. 22.

[0045] A preferred embodiment of the present invention will be described with reference to the attached drawings.

[Radio Wave Timepiece]

[0046] FIG. 1 is a block diagram illustrating a structure of the radio wave timepiece in the embodiment. According to the figure, a radio wave timepiece 1 includes a CPU (Central Processing Unit) 100, an input section 200, a display section 300, a ROM (Read Only Memory) 400, a RAM (Random Access Memory) 500, a receiving control section 600, a time-code generating section 700, a clock circuit section 800 and an oscillating circuit section 900. These sections excluding the oscillating circuit section 900 are connected to one another by a bus B. The oscillating circuit section 900 is connected to the radio wave receiving apparatus 620 and the clock circuit section 800.

[0047] The CPU 100, the ROM 400, the RAM 500, the receiving control section 600, the time-code generating section 700, the clock circuit section 800 and the oscillating circuit section 900 can be formed by using a semiconductor integrated circuit.

[0048] The CPU 100 reads out a program stored in the ROM 400 at a predetermined timing or according to an operational signal input from the input section 200, develops it on the RAM 500, and gives instructions to individual sections constituting a radio wave timepiece 1 or transfers data and the like on the basis of the program. Concretely, for example, the CPU 100 controls the receiving control section 600 every predetermined time to execute the receiving process of a standard radio wave, and to adjust the current time data to be measured by the clock circuit section 800 on the basis of a standard time code input from the time-code generating section 700.

[0049] The input section 200 is constituted with switches and the like for executing various functions of the radio wave timepiece 1, to output a corresponding operational signal to the CPU 100 when these switches are operated. The display section 300 is constituted with a small-sized liquid crystal display and the like, to display the-current time and the like on the basis of display signals input from the CPU 100.

[0050] The ROM 400 stores system programs and application programs related to the radio wave timepiece 1 as well as programs realizing the present embodiment and data. The RAM 500 is used as a working area of the CPU 100, to temporarily store programs, data and the like read out from the ROM 400.

[0051] The receiving control section 600 is provided with a radio wave receiving apparatus 620. The radio wave receiving apparatus 620 removes unnecessary frequency components of low standard radio waves received from a receiving antenna, to take out a desired frequency signal and to convert into an electrical signal to output it to the time-code generating section 700.

[0052] The time-code generating section 700 converts the electrical signal input from the radio wave receiving apparatus 620 into a digital signal and generates standard time codes including data necessary for timepiece functions such as a standard current time code, accumulated number of days from January 1, a day code and the like to output them to the CPU 100.

[0053] The clock circuit section 800 counts signals input from the oscillating circuit section 900 to measure the current time, to output the current time data to the CPU 100. The oscillating circuit section 900 is constituted with a crystal oscillator and the like, to output the reference frequency signal of 32.768 kHz.

[Radio Wave Receiving Apparatus]

[0054] FIG. 2 is a block diagram illustrating a conceptual constitution of the radio wave receiving apparatus 620 in the embodiment. According to the figure, the radio wave receiving apparatus 620 includes a receiving antenna 621, an RF amplifier circuit 622, a multi-stage frequency conversion circuit 623, a frequency divider circuit 625, a detection circuit 626 and an AGC circuit 627.

[0055] The receiving antenna 621 is constituted with, for example, a bar antenna, to receive a standard radio wave having a predetermined frequency including a current time code, and to convert the received standard radio wave into an electrical signal to output the signal. The RF amplifier circuit 622 amplifies or attenuates a signal input through the receiving antenna 621 according to a control signal “h” input from the AGC circuit 627, to output the signal.

[0056] The multi-stage frequency conversion circuit 623 has a plurality of basic circuits 624[1], 624[2] . . . , 624[N] made up of n stages connected in series (hereinafter, inclusively referred to as a basic circuit 624), to convert a signal input from the RF amplifier circuit 622 sequentially into a frequency based on such signals “g” as g1, g2, . . . gn, input from the frequency divider circuit 625 (hereinafter inclusively referred to as signal “g”), thereby to convert the signal into a lower frequency gradually to output it as signal “a”.

[0057] FIG. 3 is a view illustrating a circuit configuration of a basic circuit 624. The basic circuit 624 is a circuit (conversion circuit) for multiplying and synthesizing an input signal with a signal “g” (frequency-divided signal) input from the frequency divider circuit 625 to conduct frequency conversion. As shown in the figure, the basic circuit is constituted with a mixer 6241, a filter circuit 6242 and an amplifier 6243.

[0058] The mixer 6241 multiplies and synthesizes an input signal to the basic circuit 624 with a signal “g” input from-the frequency divider circuit 625, thereby to output the result.

[0059] The filter circuit 6242 is constituted with a LPF (low pass filter) and the like, to allow frequencies in a predetermined low range to pass through with respect to a signal input from the mixer 6241, however to cut off a frequency component outside the range. A pass band of the filter circuit 6242 is decided dependent on the frequency of an input signal and a signal “g” in the basic circuit 624. Concretely, the filter circuit 6242 is constituted in such a way that a sum frequency of the input signal and the signal “g” is cut off while a difference frequency is allowed to pass through.

[0060] The amplifier 6243 amplifies or attenuates a signal input from the filter circuit 6242 dependent on a control signal “i” input from the AGC circuit 627, to output the signal. The output of the amplifier 6243 is given as an output signal of the basic circuit 624.

[0061] The multi-stage frequency conversion circuit 623 comprises a plurality of such constituted basic circuits 624 connected serially in a multi-stage manner, and into each of the basic circuits 624, an output signal of the stage just before the each of the basic circuit 624 is input as an input signal. However, into the first stage of the basic circuit 624[1], an output signal from the RF amplifier circuit 622 is input as an input signal. Then, an output signal from the last stage of the basic circuit 624[N] is given as an output signal “a” from the multi-stage frequency conversion circuit 623.

[0062] In FIG. 2, the frequency divider circuit 625 frequency-divides or frequency-multiplies a reference frequency signal bs input from the oscillating circuit section 900 by a plurality of ratios, to output the results as signals g1, g2, . . . gn into the basic circuits 624[1], 624[2], . . . 624[N], and also to output them as a signal “f” into a detection circuit 626.

[0063] The detection circuit 626 detects a signal “a” input from the multi-stage frequency conversion circuit 623 by using the signal “f” input from the frequency divider circuit 625, and outputs it as a detected signal “d”. The detected signal “d” is input into a time-code generating section 700 and is utilized to adjust the current time and the like.

[0064] The AGC circuit 627 generates and outputs a control signal “h” to control an amplified degree of the RF amplifier circuit 622 and a control signal “i” to control an amplified degree of the amplifier 6243 in each of the basic circuits 624, depending on the strength of a signal “a” input from the multi-stage frequency conversion circuit 623.

[Detection Circuit]

[0065] FIG. 4 is a view illustrating a circuit configuration of the detection circuit 626. In this figure, the detection circuit 626 performs detection by referring to the signal “a” input from the multi-stage frequency conversion circuit 623. The detection circuit comprises a 1/2 frequency divider 6261, a logical gate 6262, mixers 6263 and 6264, LPFs 6265 and 6266, square circuits 6267 and 6268, and an adder 6269.

[0066] The 1/2 frequency divider 6261 frequency-divides the signal “f” input from the frequency divider circuit 625 into 1/2 and outputs it as a signal e1. Here, the frequency of the signal “f” which is input into the 1/2 frequency divider 6261 is set to be two times that of the signal “a”, and therefore the signal e1 which is output from the 1/2 frequency divider 6261 is equal to the frequency of the signal “a”.

[0067] The logical gate 6262 performs an exclusive OR (EOR) operation of the signal “f” with the signal e1 input from the 1/2 frequency divider 6261, to output the calculation result as a signal e2. Therefore, the signal e2 is a signal obtained by shifting the phase of the output signal e1 by 90 degrees (phase shift).

[0068] The mixer 6263 multiplies and synthesizes a signal “a” input from the multi-stage frequency conversion circuit 623 with a signal e1 input from the 1/2 frequency divider 6261, thereby to output the result. The LPF 6265 allows frequencies in a predetermined low range to pass through, with respect to a signal input from the mixer 6263, however to cut off a frequency component outside the range, and outputs a signal “b”. The square circuit 6267 squares the signal “b” input from the LPF 6265 and outputs the result.

[0069] The mixer 6264 multiplies and synthesizes a signal “a” input from the multi-stage frequency conversion circuit 623 with a signal e2 input from the logical gate 6262 and outputs the result. The LPF 6266 allows frequencies in a predetermined low range to pass through, with respect to a signal input from the mixer 6264, however, cuts off a frequency component outside the range, thereby to output it as a signal “c”. The square circuit 6268 squares the signal “c” input from the LPF 6266 and outputs the result.

[0070] The adder 6269 adds a signal input from the square circuit 6267 to a signal input from the square circuit 6268, to output the result as a detected signal d.

[0071] According to the detection circuit 626, a conversion signal whose frequency is decreased by the multi-stage frequency conversion circuit 623, a signal “f” input from the frequency divider circuit 625 and a signal obtained by performing a 90-degree phase shift to the signal “f” are multiplied and squared, and both signals are added to perform detection. Namely, a sum of squares of I and Q components of the conversion signal is calculated, thereby it enables to perform accurate detection even when a slight difference in frequency or phase between the conversion signal and a reference signal causes.

[Receiving Operation]

[0072] Next, a concrete signal-receiving operation in a radio wave receiving apparatus 620 will be explained.

(I) Reception of a Standard Radio Wave of 40 kHz (Japan):

[0073] In a case of receiving a standard radio wave of 40 kHz, a multi-stage frequency conversion circuit 623 is constituted with three stages of basic circuits, namely, 624[1], 624[2] and 624[3]. FIG. 5A to FIG. 5D and FIG. 6 are views illustrating an image of frequency spectrum for explaining a signal-receiving operation in this case.

[0074] First, a received signal of 40 kHz from the RF amplifier circuit 622 and a signal g1 of 32.768 kHz which is a reference frequency signal bs output from the frequency divider circuit 625 are input into the first stage of the basic circuit 624[1] in the multi-stage frequency conversion circuit 623. Next, as illustrated in FIG. 5A, the mixer 6241 multiplies and synthesizes the received signal of 40 kHz with the signal g1 of 32.768 kHz to generate a signal of 72.768 kHz and a signal of 7.232 kHz, which are a sum of and a difference between these two frequencies, respectively.

[0075] Here, when a cut-off frequency of a filter circuit 6242 in the basic circuit 624[1] is about 8 kHz, in the generated signals by the mixer, a signal of 72.768 kHz is cut off by the filter circuit 6242, and a signal of 7.232 kHz passes through the filter circuit 6242 to output as an output signal of the basic circuit 624[1] via an amplifier 6243.

[0076] In other words, the basic circuit 624[1] is equivalent to a BPF (band pass filter) which includes 40 kHz of the input signal in a pass band. Further, a bandwidth of the equivalent BPF is dependent on the bandwidth of the filter circuit 6242.

[0077] Into the next stage of the basic circuit 624[2], a signal of 7232 Hz output from the basic circuit 624[1] being the previous stage and a signal g2 of 8192 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 4 the signal of 32768 Hz which is a reference frequency signal bs are input. As illustrated in FIG. 5B, the input signal of 7232 Hz and the signal g2 of 8192 Hz are multiplied and synthesized to generate a signal of 15424 Hz and a signal of 960 Hz, which are a sum of and a difference between these two frequencies, respectively.

[0078] Here, when a cut-off frequency of a filter circuit 6242 in the basic circuit 624[2] is about 1 kHz, in the generated signals by the mixer, a signal of 15424 Hz is cut off by the filter circuit 6242, and a signal of 960 Hz passes through the filter circuit 6242 to output as an output signal of the basic circuit 624[2] via an amplifier 6243.

[0079] In other words, the basic circuit 624[2] is equivalent to a BPF which includes 3272 Hz of the input signal in a pass band. Further, the pass band of the equivalent BPF is dependent on the pass band of the filter circuit 6242. However, since the pass band of the filter circuit 6242 in the basic circuit 624[2] is narrower than that of the filter circuit 6242 in the basic circuit 624[1], the pass band of the equivalent BPF in the basic circuit 624[2] is narrower than that of the equivalent BPF in the basic circuit 624[1].

[0080] Into the final stage of the basic circuit 624[3], a signal of 960 Hz output from the basic circuit 624[2] being the previous stage and a signal g7 of 1024 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 32 the signal of 32768 Hz which is a reference frequency signal bs are input. As illustrated in FIG. 5C, the input signal of 960 Hz and the signal g7 of 1024 Hz are multiplied and synthesized to generate a signal of 1984 Hz and a signal of 64 Hz, which are a sum of and a difference between these two frequencies, respectively.

[0081] Here, when a cut-off frequency of the filter circuit 6242 in the basic circuit 624[3] is about 70 Hz, in the generated signals by the mixer, a signal of 1984 Hz is cut off by the filter circuit 6242, and a signal of 64 Hz passes through the filter circuit 6242 to output as an output signal of the basic circuit 624[3]. The output signal is input into the detection circuit 626 as the output signal of the multi-stage frequency conversion circuit 623.

[0082] In other words, the basic circuit 624[3] is equivalent to a BPF which includes 1024 Hz of the input signal in a pass band. Further, the pass band of the equivalent BPF is dependent on the pass band of the filter circuit 6242. However, since the pass band of the filter circuit 6242 in the basic circuit 624[3] is narrower than that of the filter circuit 6242 in the basic circuit 624[2], the pass band of the equivalent BPF in the basic circuit 624[3] is narrower than that of the equivalent BPF in the basic circuit 624[2].

[0083] Then, into the detection circuit 626, the signal “a” of 64 Hz output from the multi-stage frequency conversion circuit 623 and the signal g11 of 128 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 256 the signal of 32768 Hz which is the reference frequency signal bs, are input and detected. That is, as illustrated in FIG. 5D, the mixers 6263 and 6264 multiply and synthesize the input signal “a” of 64 Hz and signals e1 of 64 Hz, and the input signal “a” and e2 of 64 Hz which is different from e1 in phase by 90 degrees, respectively, to generate a signal of 128 Hz and a signal of 0 Hz, which are a sum of and a difference between these two frequencies, respectively.

[0084] Here, when a cut-off frequency of each of the LPFs 6265 and 6266 is about 5 Hz, in the generated signals by the mixers, a signal of 128 Hz is cut off by the LPFs 6265 and 6266, and a signal of 0 Hz passes through the filter circuit 6242 to output as an output signal of the LPFs 6265 and 6266. The output signals are squared by square circuits 6267 and 6268, and further added to output as a detected signal “d”.

[0085] In other words, the detection circuit 626 is equivalent to a BPF which includes 64 Hz in a pass band. Further, the pass band of the equivalent BPF is dependent on the pass band of the filter circuit 6242. However, since the pass band of the LPFs 6265 and 6266 is narrower than that of the filter circuit 6242 in the basic circuit 624[3], the pass band of each LPF is narrower than that of the equivalent BPF in the basic circuit 624[3].

[0086] Therefore, the radio wave receiving apparatus 620 is, as a whole, equivalent to four stages of BPF connected in series. As illustrated in FIG. 6, it can be regarded as a BPF having an extremely narrow band centered on 40 kHz, which is a reception frequency. FIG. 6 is a view on an assumption that an operation of receiving standard radio waves given in FIG. 5A to FIG. 5D is regarded as a BPF having an extremely narrow band or as a comprehensive BPF.

[0087] In the multi-stage frequency conversion circuit 623, an input signal output from the basic circuit 624 of the stage just before each of the basic circuits 624 is multiplied and synthesized with signals “g” (g2, g4 and g7) to decrease the frequency, so that the frequency of the received signal input from the RF amplifier circuit 622 is gradually decreased. That is, since the pass bands of the equivalent BPF of the basic circuits 624 are gradually narrower, the radio wave receiving apparatus 620 in its entirety can be regarded as a BPF having an extremely narrow band centered on the frequency of the received signal.

[0088] Although an ideal signal-receiving operation in the radio wave receiving apparatus 620 is described above, the signal “a” input into the detection circuit 626 is actually not in perfect coincident with the signal “f” in frequency and phase, and thereby results in a possible deformation of the waveform of a detected signal “d”. In the embodiment, however, the sum of squares of I and Q components of the signal “a” is calculated at the detection circuit 626, thereby to make it possible to prevent the deformation of a waveform of the detected signal “d” resulting from the deviation and to perform accurate detection.

[0089] Next, a concrete explanation thereof will be made.

[0090] In FIG. 4, when a signal “a” which is input into the detection circuit 626, is expressed by a=A sin ωt, a signal e1 output from the 1/2 frequency divider 6261 has the same frequency as that of the signal “a” and is therefore expressed to be e1=sin(ωt+φ (t)). Here, φ (t) is a phase lag (difference) from the signal “a”. Therefore, an output signal of the mixer 6263 is expressed by the following equation (1). $\begin{array}{c}a·e1=A\sin \varpi t·\sin \left(\varpi t+\varphi \left(t\right)\right)\\ =\frac{A}{2}\left\{\cos \varphi \left(t\right)-\cos 2\varpi t·\cos \varphi \left(t\right)+\sin 2\varpi t·\cos \varphi \left(t\right)\right\}\end{array}\left(1\right)$

[0091] When the signal passes through the LPF 6265, high-frequency components are cut off, and the signal “b” output from the LPF 6265 is expressed by b=A/2·cos φ (t) The signal e2 is a signal obtained by shifting the phase of the signal e1 by 90 degrees, and expressed by e2=cos (ωt+φ (t)). Therefore, an output signal of the mixer 6264 is expressed by the following equation (2). $\begin{array}{cc}\begin{array}{c}a·e2=A\sin \varpi t·\cos \left(\varpi t+\varphi \left(t\right)\right)\\ =\frac{A}{2}\left\{\sin 2\varpi t·\cos \varphi \left(t\right)-\sin \varphi \left(t\right)+\cos 2\varpi t·\sin \varphi \left(t\right)\right\}\end{array}& \left(2\right)\end{array}$

[0092] When the signal passes through the LPF 6266, high-frequency components are cut off, and the signal “c” output from the LPF 6266 is expressed by c=−A/2·sin φ (t).

[0093] Then, signals b and c are squared by the square circuits 6267 and 6268, respectively, and added by an adder 6269 to output a detection signal “d” from the detection circuit 626. The detection signal “d” is expressed by the following equation (3). $\begin{array}{cc}\begin{array}{c}d={\left\{\frac{A}{2}\cos \varphi \left(t\right)\right\}}^2+{\left\{-\frac{A}{2}\sin \varphi \left(t\right)\right\}}^2\\ =\frac{A^2}{4}\left\{{\cos }^2\varphi \left(t\right)+{\sin }^2\varphi \left(t\right)\right\}\\ =\frac{A^2}{4}\end{array}& \left(3\right)\end{array}$
(II) Reception of a standard Radio Wave of 77.5 kHz (Germany)

[0094] In a case of receiving a standard radio wave of 77.5 kHz, the multi-stage frequency conversion circuit 623 is constituted with five stages of basic circuits, namely, 624[1], 624[2] . . . 624[5]. FIG. 7A to FIG. 7D, FIG. 8A to FIG. 8B and FIG. 9 are views illustrating images of frequency spectrum for explaining a signal-receiving operation in this case.

[0095] First, a received signal of 77.5 kHz from the RF amplifier circuit 622 and a signal g1 of 65.536 kHz obtained by multiplying by 2 a signal of 32.768 kHz which is a reference frequency signal bs output from the frequency divider circuit 625 are input into the first stage of the basic circuit 624[1]. Next, as illustrated in FIG. 7A, the mixer 6241 multiplies and synthesizes the received signal of 77.5 kHz with the signal g1 of 65.536 kHz, to output a signal of 11.964 kHz which is the difference between these two frequencies, as an output signal of the basic circuit 624[1], after passing through the filter circuit 6242. In this case, the basic circuit 624[1] can be regarded to be equivalent to a BPF which includes 77.5 kHz of the input signal in a pass band.

[0096] Into the next stage of the basic circuit 624[2], a signal of 11964 Hz output from the basic circuit 624[1] being the previous stage and a signal g4 of 8192 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 4 the signal of 32768 Hz which is a reference frequency signal bs are input. As illustrated in FIG. 7B, the input signal of 11964 Hz and the signal g4 of 8192 Hz are multiplied and synthesized and a signal of 3772 Hz which are a difference between these two frequencies passes through the filter circuit 6242 to output as the output signal of the basic circuit 624[2]. In this case, the basic circuit 624[2] can be regarded to be equivalent to a BPF which includes 8192 Hz of the input signal in a pass band. The pass band of the equivalent BPF is narrower than that of the equivalent BPF in the basic circuit 624[1].

[0097] Into the next stage of the basic circuit 624[3], a signal of 3772 Hz output from the basic circuit 624[2] being the previous stage and a signal g5 of 8192 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 8 the signal of 32768 Hz which is a reference frequency signal bs are input. As illustrated in FIG. 7C, the input signal of 3372 Hz and the signal g4 of 4096 Hz are multiplied and synthesized to generate a signal of 324 Hz which is the difference between these two frequencies. The signal of 324 Hz passes through the filter circuit 6242 and outputs as the output signal of the basic circuit 624[3]. In this case, the basic circuit 624[3] can be regarded to be equivalent to a BPF which includes 3372 Hz of the input signal in a pass band. The pass band of the equivalent BPF is narrower than that of the equivalent BPF in the basic circuit 624[2].

[0098] Into the next stage of the basic circuit 624[4], a signal of 324 Hz output from the basic circuit 624[3] being the previous stage and a signal “g9” of 256 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 128 the signal of 32768 Hz which is a reference frequency signal are input. As illustrated in FIG. 7D, the signal of 324 Hz and the signal g4 of 256 Hz are multiplied and synthesized to generate a signal of 68 Hz which is the difference between these two frequencies. The signal of 68 Hz passes through the filter circuit 6242 and outputs as the output signal of the basic circuit 624[4]. In this case, the basic circuit 624[4] can be regarded to be equivalent to a BPF which includes 324 Hz of the input signal in a pass band. The pass band of the equivalent BPF is narrower than that of the equivalent BPF in the basic circuit 624[3].

[0099] Into the final stage of the basic circuit 624[5], a signal of 68 Hz output from the basic circuit 624[4] being the previous stage and a signal g11 of 64 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 512 the signal of 32768 Hz which is a reference frequency signal are input. As illustrated in FIG. 8A, the signal of 68 Hz and the signal g11 of 64 Hz are multiplied and synthesized to generate a signal of 4 Hz which is the difference between these two frequencies. The signal of 4 Hz passes through the filter circuit 6242 and outputs as the output signal of the basic circuit 624[5]. This output signal is also the output signal of the multi-stage frequency conversion circuit 623. In this case, the basic circuit 624[5] can be regarded to be equivalent to a BPF which includes 68 Hz of the input signal in a pass band. The pass band of the equivalent BPF is narrower than that of the equivalent BPF in the basic circuit 624[3].

[0100] Then, into the detection circuit 626, the signal “a” of 4 Hz output from the multi-stage frequency conversion circuit 623 and the signal g15 as a signal “f”, of 4 Hz output from the frequency divider circuit 625, obtained by frequency-dividing by 8182 the signal of 32768 Hz which is the reference frequency signal bs, are input and detected. That is, as illustrated in FIG. 8B, the input signal “a” of 4 Hz and the signal “f” of 4 Hz are multiplied and synthesized to generate a signal of 0 Hz which a difference between these two frequencies. The generated signal is output as a detection signal “d” output from the detection circuit 626. In this case, the detection circuit 626 can be regarded to be equivalent to a BPF which includes 4Hz of the input signal in a pass band. The pass band of the equivalent BPF is narrower than that of the equivalent BPF in the basic circuit 624[5].

[0101] Therefore, the radio wave receiving apparatus 620 is, as a whole, equivalent to 6 stages of BPF connected in series. As illustrated in FIG. 9, it can be regarded as a BPF having an extremely narrow band centered on 77.5 kHz, which is a reception frequency. FIG. 9 is a view on an assumption that an operation of receiving standard radio waves given in FIG. 7A to FIG. 7D and FIG. 8A to FIG. 8B is regarded as a BPF having an extremely narrow band or as a comprehensive BPF.

[0102] Additionally, since the signal “a” output from the last stage of the basic circuit 624[5] has a low frequency of 4 Hz, the multi-stage frequency conversion circuit 623 may be constituted with four stages of basic circuits 624[1], 624[2], . . . and 624[4]. In this case, a signal “a” of 68 Hz from the multi-stage frequency conversion circuit 623 and a signal “f” of 64 Hz from the frequency divider circuit 625 are respectively input into the detection circuit 626 to perform detection. Then, although a detected signal “d” of 4 Hz which is a difference between these two frequencies, is output, since the detection circuit 626 is used to detect only amplitude components of signals, there are no problem for detection, namely, for reproduction of received signals.

[0103] FIG. 10 is a table showing frequencies of signals “g” input from the frequency divider circuit 625 into each of the basic circuits 624 in the multi-stage frequency conversion circuit 623 and frequencies of output signals of the basic circuit 624 when receiving standard radio waves different in frequency in various countries. This figure shows the following cases, 1) Japan (40 kHz), 2) Japan (60 kHz), 3) Germany (77.5 kHz), 4) Switzerland (70 kHz) and 5) China (68.5 kHz).

[0104] For example, in the case of 2) Japan (60 kHz), the multi-stage frequency conversion circuit 623 is constituted with five stages of basic circuits, namely, 624[1], 624[2], . . . , 624[5]. In the first stage of the basic circuit 624[1], a received signal of 60 kHz and a signal g1 of 65.536 kHz are multiplied and synthesized, and converted into a signal of 5536 Hz which is a difference frequency therebetween. Then, in the basic circuit 624[2], the signal of 5536 Hz and a signal g4 of 8192 Hz are multiplied and synthesized, and converted into a signal of 2656 Hz. In the next stage of the basic circuit 624[3], the signal of 2656 Hz and a signal “g6” of 2048 Hz are multiplied and synthesized, and converted into a signal of 608 Hz. Subsequently, in the basic circuit 624[4], the signal of 608 Hz and a signal “g8” of 512 Hz are multiplied and synthesized, and converted into a signal of 96 Hz, in the basic circuit 624[5], the signal of 96 Hz and a signal “g10” of 128 Hz are multiplied and synthesized, and converted into a signal of 32 Hz. Then, the signal of 32 Hz and a signal “g12” of 32 Hz as a signal “f” are input into the detection circuit 626 to perform detection.

[0105] As described above, n-stages of basic circuits 624 connected in series in the multi-stage frequency conversion circuit 623 convert standard radio waves received from the receiving antenna 621 into lower frequencies sequentially on the basis of signals “g” input from the frequency divider circuit 625. Then, signals output from the multi-stage frequency conversion circuit 623 are detected by the detection circuit 626.

[0106] According to the embodiment of the invention, local oscillating circuits or PLL circuits which were required in a conventional super-heterodyne system of radio wave receiving apparatus are not necessary. Therefore, it is possible to receive signals in a stable manner and to reduce electric power consumption for a whole apparatus. Further, because the process in which frequencies of received signals are converted into frequencies based on a frequency-divided signal is conducted by a plurality of conversion circuits, it is possible to receive signals with a high accuracy. In addition, since each of conversion circuits for converting frequencies are constituted with simple circuit elements, a reduction in chip size is attained according to a large-scale integration by using CMOS.

[0107] Next, embodiments of the radio wave receiving apparatus 620 according to the invention will be explained concretely.

[0108] First, Embodiment 1 will be explained as follows.

[0109] As described above, a multi-stage frequency conversion circuit 623 is constituted with a plurality of basic circuits 624 connected in series. Each of the basic circuits 624 is different from one another in pass band set in a filter circuit 6242, depending on a frequency of a standard radio wave to be received and a stage at which the basic circuit 624 is arranged in the multi-stage frequency conversion circuit 623. Therefore, in Embodiment 1, the individual basic circuits 624 are constituted as follows.

[0110] FIG. 11A is a view illustrating a circuit configuration of the basic circuit 624A in Embodiment 1. In the figure, the basic circuit 624A includes a mixer 6241, a filter circuit 6242A and an amplifier 6243. The filter circuit 6242A is provided with registers R1 and R2 connected in series, a capacitor C and a switch SW1 connected to the register R2 in parallel. The switch SW1 is operated by an input from a CPU 100, for example. ON/OFF (connection/disconnection) is controlled by a bandwidth switching signal SW1-1 for instructing to switch a pass band of the filter circuit 6242A.

[0111] In the basic circuit 624A, when the switch SW1 is ON, a signal input from the mixer 6241 to the filter circuit 6242A passes through the register R1 and the switch SW1 to output, while the filter circuit 6242A functions as an RC filter having the register R1 and the capacitor C. In contrast, when the switch SW1 is OFF, a signal input into the filter circuit 6242A passes through the registers R1 and R2, and is output, while the filter circuit 6242A functions as an RC filter having the registers R1, R2 and the capacitor C. More specifically, the switch SW1 is turned ON/OFF by a bandwidth switching signal to be input, and thereby a time constant of the filter circuit 6242A is changed, or a pass band is switched.

[0112] Here, the filter circuit 6242A may be set for a pass band so as to cut off a sum frequency of an input signal to the basic circuit 624 and a signal “g” and also allow a difference frequency to pass through. Therefore, it is possible to realize a radio wave receiving apparatus 620 which enables conversion to a larger scale integration easily and general use, by providing the multi-stage frequency conversion circuit 623 which has a plurality of basic circuits 624A with the same constitution, connected in series, and in which for example, a bandwidth switching signal input from the CPU 100 is used for setting a pass band of each of the basic circuits 624.

[0113] Additionally, the filter circuit 6242A may be constituted with three or more registers R, in place of the registers R1 and R2. FIG. 11B is a view illustrating an example of a circuit configuration of the basic circuit 624A-1 having 3 or more registers R. According to FIG. 11B, in the basic circuit 624A-1, the filter circuit 6242A-1 is constituted with a register R1, registers R2a, R2b, R2c . . . connected in parallel, a capacitor C, a switch SW6 connected in parallel to the registers R2a, R2b, R2c, . . . and switches SW6a, SW6b , SW6c, . . . connected to the registers R2a, R2b, R2c . . . in series, respectively. These switches SW6, SW6a, SW6b , SW6c, . . . are controlled for ON/OFF by switching control signals (SW6-1, SW6a-2, SW6b -3, SW6c-4, . . . ) input from the CPU 100, for example. Thereby, it is possible to set a pass band of the filter circuit 6242A-1 so as to be switched to 3 or more stages.

[0114] According to an invention of Embodiment 1, filters equipped in the basic circuits connected in series are allowed to be alternatively switched to a pass band among a plurality of predetermined pass bands. Therefore, these basic circuits can be constituted to have the same structure, for example, a pass band is switched depending on a frequency of a received signal and the stage at which the basic circuit is arranged in the multi-stage frequency conversion circuit, thereby to make it possible to provide an apparatus with a general-purpose constitution.

[0115] Next, Embodiment 2 will be explained as follows.

[0116] Embodiment 2 is one of a so-called multiband apparatus in which a radio wave receiving apparatus 620 is capable of receiving a plurality of different frequencies of standard radio waves.

[0117] FIG. 12 is a block diagram illustrating a constitution of the radio wave receiving apparatus 620B according to Embodiment 2. In this figure, the radio wave receiving apparatus 620B includes a receiving antenna 621, an RF amplifier circuit 622, a multi-stage frequency conversion circuit 623B, a frequency divider circuit 625B, a detection circuit 626 and an AGC circuit 627.

[0118] Here, an explanation will be omitted for a block of functions and constitutions which is similar to that explained in FIG. 2.

[0119] The multi-stage frequency conversion circuit 623B is constituted with N-stages of a plurality of basic circuits 624[1], 624[2], . . . 624[N]. Then, signals g1, g2, . . . “gN” from the frequency divider circuit 625B are input into the basic circuits 624[1], 624[2], . . . , 624[N], respectively, and for example, a use/non-use switching signal sf is input from the CPU 100.

[0120] The frequency divider circuit 625B outputs signals g1, “g2”, . . . , “gN” obtained by dividing a reference frequency signal bs input from a transmitting circuit section 900 by the respective frequency dividing ratios, 2, 1, 1/2, 1/4, . . . 1/2^(N−2) (N is an integral number) and a signal “f”. Additionally, the frequency divider circuit 625B performs frequency-dividing after the reference frequency signal bs is multiplied by 2. However, for simplifying the explanation, an explanation will be made on the assumption that basic frequencies are to be divided.

[0121] Here, the number of stages N on the multi-stage frequency conversion circuit 623B is dependent on a frequency of the reference frequency signal bs. Namely, for example, when the reference frequency signal bs is a signal of 32.768 kHz, the multi-stage frequency conversion circuit 623B is constituted with serially-connected 16 stages of the basic circuits 624[1], 624[2], . . . , 624[16]. Then, as illustrated in the table given in FIG. 10, signals g1, g2, . . . , “g16” having 65768, 32768, 16384, 8192, . . . , 4 and 2 Hz, obtained by frequency-dividing the signal of 32768 Hz by the respective frequency dividing ratios of 2, 1, 1/2, 1/4, . . . , 1/8182 and 1/16384, respectively, is output from a frequency divider circuit 625. These signals g1, g2, . . . , “g16” are input into basic circuits 624[1], 624[2], . . . , 624[16], respectively.

[0122] The use/non-use switching signal sf means a signal for specifying the use/non-use of individual basic circuits 624[1], 624[2], . . . , 624[N]. “To use” the basic circuits 624[1], 624[2], . . . , 624[N] means that in the basic circuit 624 concerned, synthesis is made by multiplying a signal “g” input from the frequency divider circuit 624 by an input signal from the previous stage to decrease the frequency, namely, to perform frequency conversion, while “not to use” the basic circuits (non-use) means that an input signal is output with no frequency conversion performed in the input signal. Whether individual basic circuits 624[1], 624[2], . . . , 624[N] which constitute the multi-stage frequency conversion circuit 623B are used or not is dependent on the frequency of a standard radio wave to be received.

[0123] For example, (A) when a standard radio wave of 40 kHz is received, as explained by referring to FIG. 5A to FIG. 5D and FIG. 6, the basic circuit 624[1] into which a signal g2 of 32768 Hz (being a reference frequency signal bs) is input, the basic circuit 624[2] into which a signal g4 of 8192 Hz obtained by frequency-dividing by 4 is input, and the basic circuit 624[3] into which a signal g7 of 1024 Hz obtained by frequency-dividing by 32 is input, are “used”. On the contrary, basic circuits 624[4], 624[5], . . . , 624[N] other than the above-described three basic circuits are “not used.”

[0124] (B) When a standard radio wave of 77.5 kHz is received, as explained by referring to FIG. 7A to FIG. 7D, FIG. 8A to FIG. 8B and FIG. 9, five basic circuits 624, into which a signal g1 of 65536 Hz obtained by multiplying a reference frequency signal bs by 2 is input, a signal g4 of 8192 Hz obtained by frequency-dividing the signal by 4 is input, a signal g5 of 4096 Hz obtained by frequency-dividing the signal by 8 is input, a signal “g9” of 256 Hz obtained by frequency-dividing the signal by 128 is input, and a signal g11 of 64 Hz by frequency-dividing the signal by 512 is input; are “used”. On the contrary, the basic circuits 624 other than the five above-described basic circuits are “not used.”

[0125] FIG. 13A is a view illustrating a basic circuit 624B, which is one circuit configuration, among basic circuits 624[1], 624[2], . . . , 624[N] constituting the multi-stage frequency conversion circuit 623B in Embodiment 2. According to FIG. 13A, the basic circuit 624B is constituted with switches SW2, SW3, a mixer 6241, a filter circuit 6242 and an amplifier 6243.

[0126] The switch SW2 is provided at the previous stage of the mixer 6241 and connected to either of terminals a or b, depending on a use/non-use switching control signal sf input from a CPU 100. The switch SW3 is provided at the subsequent stage of the amplifier 6243, and connected to either of the terminals “aa” or “b”, depending on the use/non-use switching control signal sf to be input.

[0127] FIG. 13B is a table illustrating the relationship between the use/non-use switching signal sf and the connection state of switches SW2 and SW3. According to FIG. 13B, when the switching signal specifies the use, the switch SW2 is connected to the terminal “a”, while the switch SW3 is connected to the terminal “a”. Therefore, the input signal is multiplied and synthesized with a signal “g” input from the frequency divider circuit 625 by the mixer 6241 and is frequency-converted. The frequency-converted signal passes through the filter circuit 6242 and the amplifier 6243 to output as an output signal of the basic circuit 624B. Namely, the basic circuit 624 is in a state of “use.”

[0128] When the use/non-use switching signal sf specifies “non-use”, the switch SW2 is connected to the terminal “b”, while the switch SW3 is connected to the terminal “b”. Therefore, the input signal is not subjected to frequency conversion but output as an output signal of the basic circuit 624, without any change. Namely, the basic circuit 624 is in a “non-use” state.

[0129] As described above, according to Embodiment 2, the multi-stage frequency conversion circuit 623B is constituted with a plurality of basic circuits 624B identical in constitution, and a use/non-use switching signal sf input externally is used to switch the use/non-use of individual basic circuits 624B. Therefore, the use/non-use switching signal sf is set in accordance with a frequency of a standard radio wave to be input, thereby to make it possible to provide a general-purpose radio wave receiving apparatus 620 in which only the necessary basic circuit 624B is used but other basic circuits 624 are not used.

[0130] Next, an explanation will be made for Embodiment 3.

[0131] Similarly to Embodiment 2 described above, Embodiment 3 is an embodiment of a multiband radio wave receiving apparatus 620, and different from Embodiment 2 in that the basic circuit 624B shown in FIG. 13A is replaced by the basic circuit 624C shown in FIG. 14A.

[0132] FIG. 14A is a view illustrating a circuit configuration of a basic circuit 624C in Embodiment 3. In FIG. 14A, the basic circuit 624C is constituted with a mixer 6241, a filter circuit 6242C, an amplifier 6243 and a switch SW4.

[0133] The switch SW4 is provided between the mixer 6241 and the frequency divider circuit 625, and controlled for ON/OFF in accordance with a use/non-use switching control signal sf input from the CPU 100.

[0134] The filter circuit 6242C is provided with serially-connected registers R1 and R2, a capacitor C and a switch SW5 connected in parallel to the register R2. Herein, the switch SW5 is controlled for ON/OFF in accordance with a use/non-use switching signal input from the SW5.

[0135] FIG. 14B is a view illustrating the relationship between the use/non-use switching signal sf and the connection state of the switch SW5. According to FIG. 14B, when “use” is specified by the use/non-use switching signal sf, the switch SW4 is turned on, while the switch SW5 is turned off. Therefore, the mixer 6241 performs synthesis by multiplying the input signal by a signal “g” input from the frequency divider circuit 625 to perform frequency conversion, and outputs as an output signal of the basic circuit 624C. Further, in this case, the filter circuit 6242C functions as a low pass filter having a pass band dependent on the respective register values of the registers R1, R2 and a capacitance value of the capacitor C. Namely, the basic circuit 624 is in a “use” state.

[0136] Further, when “non-use” is specified by the use/non-use switching signal sf, the switch SW4 is turned off and the switch SW5 is turned on. Therefore, since a signal “g” from the frequency divider circuit 625 is not input into the mixer 6241, an input signal is not subjected to frequency conversion but passes through the filter circuit 6242C and outputs as an output signal. Namely, the basic circuit 624 is in a state of “non-use.” In this case, the filter circuit 6242C is given as a RC filter made up of the register R1 and the capacitor C, but the register R1 is so small in register value that it will not actually function as a filter.

[0137] As described above, according to Embodiment 3, the multi-stage frequency conversion circuit 623 is constituted with a plurality of basic circuits 624C identical in constitution, and a use/non-use switching signal input from the outside is used to switch the use/non-use of individual basic circuits 624C. Therefore, the use/non-use switching signal sf is set in accordance with a frequency of a standard radio wave to be received, thereby to make it possible to provide a general-purpose radio wave receiving apparatus 620, in which only the necessary basic circuits 624C are used but other basic circuits 624C are not used.

[0138] Next, an explanation will be made for Embodiment 4.

[0139] FIG. 15 is a block diagram illustrating a schematic constitution of a radio wave receiving apparatus 620D in Embodiment 4. In the figure, the radio wave receiving apparatus 620D is constituted with a receiving antenna 621, an RF amplifier circuit 622, a multi-stage frequency conversion circuit 623, a frequency divider circuit 625D, a detection circuit 626, an AGC circuit 627 and a switch group 628.

[0140] An explanation will be omitted for a block of functions and constitutions which is similar to that explained in FIG. 2.

[0141] The frequency divider circuit 625D is provided with a plurality of output terminals of t1, t2, t3, . . . , tm for outputting signals g1, g2, g3, . . . , gm obtained by frequency-dividing a reference frequency signal bs input from the transmitting circuit section 900 by the frequency dividing ratios of 2, 1, 1/2, 1/4, . . . , 1/2^(m−2) (m is an integral number), respectively.

[0142] The switch group 628 comprises a plurality of switches S1, S2, . . . , Sn provided between the respective basic circuits 624[1], 624[2], . . . , 624[N] in the multi-stage frequency conversion circuit 623 and the frequency divider circuit 625, and switches Sn+l provided between the detection circuit 626 and the-frequency divider circuit 625; These switches S1, S2, . . . , Sn+1 are respectively connected to any one of the output terminals t1, t2, t3, . . . , tm of the frequency divider circuit 625, for example, in accordance with a selected signal “st” input from a CPU 100.

[0143] As described above, in a case of a multiband radio wave receiving apparatus 620, a frequency of a signal “g” input into each of the basic circuits 624 in the multi-stage frequency conversion circuit 623 is different, depending on the frequency of a standard radio wave to be received. Therefore, similarly to Embodiment 4, a selected signal “st” input from outside is used to switch the connection of each of the switches S in the switch group 628 provided between each of the basic circuits 624 and the detection circuit 626, and the frequency divider circuit 625, thereby to make it possible to switch a frequency of a signal “g” input into the basic circuits 624[1], 624[2] 624[N] and to provide a multiband radio wave receiving apparatus 620 with a general-purpose composition.

[0144] Further, each of these conversion circuits is made identical in constitution, for example, a frequency-divided signal is switched depending on a frequency of the received signal or a stage at which the conversion circuit is positioned in a plurality of serially-connected conversion circuits, thereby to make it possible to provide a general-purpose constitution.

[0145] Next, an explanation will be made for Embodiment 5.

[0146] As described above, at each of the basic circuits 624 in the multi-stage frequency conversion circuit 623, an input signal is frequency-converted (down conversion) on the basis of a frequency-divided signal “g”. However, there may be a problem of generating an image signal resulting from the frequency conversion.

[0147] For example, when a signal of frequency ω is received, frequency conversion performed by using a frequency-divided signal of frequency ω1 as a local signal will result in a fact that a signal of frequency (image signal 1) positioned symmetrically to a desired signal to be received with respect to the frequency ω1, on a frequency axis, in addition to a signal of the desired frequency ω to be received (the desired signal), as illustrated in FIG. 17A.

[0148] Next, when performing an additional frequency conversion by using a frequency-divided signal of frequency ω2 as a local signal, as illustrated in FIG. 17, a frequency conversion is performed for each of the desired signal to be received and the image signal 1. Namely, by the frequency conversion for the desired signal to be received, a signal of frequency (image signal 2) positioned symmetrically to the desired signal to be received, with respect to the frequency ω2 is also received. Further, by the frequency conversion for the image signal 1, a signal of frequency (image signal 3) positioned symmetrically to the image signal 1, with respect to the frequency ω2_i is received. The frequency ω2_i is a frequency positioned symmetrically to the frequency of ω2 with respect to the frequency ω1.

[0149] Namely, by two-stages frequency conversion, a total of 4 signals which include one desired signal to be received and three image signals 1 to 3 are received. Therefore, when n-stages of the frequency conversion are performed, an additional number (2ⁿ−1) of image signals are received, in addition to a desired signal to be received.

[0150] Therefore, in Embodiment 5, in order to remove these image signals, each of the basic circuits 624 is constituted as follows. FIG. 18 is a view illustrating a circuit configuration of a basic circuit 624F in Embodiment 5. According to the figure, the basic circuit 624F is constituted with a phase shifter 6244, mixers 6245a, 6245b, phase-shift circuits 6246a, 6246b , an adder-subtractor 6247 and a filter circuit 6248.

[0151] The phase shifter 6244 performs a 90-degree phase shift to a signal “g” input from the frequency divider circuit 625, thereby to output it as a signal “g_i”. The mixer 6245a makes synthesis by multiplying an input signal into the basic circuit 624F by a signal “g”, thereby to output them as a signal “f_1I”. The mixer 6245b makes synthesis by multiplying an input signal by a signal “g_i” input from the phase shifter 6244, thereby to output them as a signal “f_1Q”.

[0152] The phase-shift circuit 6246a allows a signal “f_1I” input from the mixer 6245a to undergo phase shift, thereby to output it as a signal “f_2I”. The phase-shift circuit 6246b allows a signal “f_1Q” input from the mixer 6245b to undergo phase shift, thereby to output it as a signal “f_2Q”. Herein, the phase-shift circuits 6426a and 6246b are constituted in such a way that a difference in phase shift (difference in phase shift angle) between the phase-shift circuit 6246a and the 6246b is at 90 degrees (π/2). For example, where the phase-shift circuit 6246a allows the signal “f_1I” to undergo “α” phase shift, the phase-shift circuit 6246b is constituted so as to allow the signal “f_1Q” to undergo “α-π/2” phase shift.

[0153] FIG. 19 is a view illustrating the circuit configurations of the phase-shift circuit 6246a and 6246b. As given in the figure, the phase-shift circuits 6246a and 6246b are identical in constitution and constituted with a two-stage APF (All Pass Filter) 6247 connected in series. The APF 6247 is a filter which allows only a phase to change and is provided with an operational amplifier OP, registers R1, R2, and R3 and a capacitor C1. An output level of the APF 6247 is dependent on values of the registers R1 and R2, and a phase shift level of the APF 6247 is dependent on those of the register R3 and the capacitor C1. Since a one-stage APF 6247 can perform a phase shift up to 180 degrees, the phase-shift circuits 6246a and 6246b comprising a two-stage APF 6247 can perform a phase shift up to 360 degrees.

[0154] In FIG. 18, the adder-subtractor 6247 makes synthesis by adding or subtracting a signal “f_2I” input from the phase-shift circuit-6246a to or from a signal “f_2Q” input from the phase-shift circuit 6246b, thereby to output them as a signal “f₃”, for example, depending on a sum/difference switching signal wsk input from a CPU 100.

[0155] The filter circuit 6248 is an LPF (Low Pass Filter), allowing frequencies in a predetermined low range to pass through with respect to a signal “f₃” input from the adder-subtractor 6247, while cutting off frequency components beyond the range. The filter circuit 6248 includes serially-connected registers R4 and R5, a capacitor C2 and a switch SW1 connected in parallel to the register R4. The switch SW1 is controlled for ON/OFF, for example, depending on a time constant switching signal tk input from the CPU 100. The switch SW1 is switched ON/OFF, thereby to change a time constant of the filter circuit 6248, namely, to switch a pass band. An output signal from the filter circuit 6248 is given as an output signal of a basic circuit 624F.

[0156] The basic circuit 624F generates input signals of I and Q signals, allows the generated Q signal to undergo a 90-degreephase shift with respect to the I signal to effect synthesis, thereby removing an image signal. FIG. 20A and FIG. 20B are views for explaining a principle of removing an image signal by the basic circuit 624F, a lengthwise direction is given as a real axis (I component), and an oblique depth direction is given as an imaginary axis (Q component) to indicate a concept of the phase-shift relationship between a desired signal to be received and an image signal. Further, the solid line indicates the desired signal to be received and the dotted line indicates the image signal.

[0157] As illustrated in FIG. 20A, a desired signal to be received and an image signal respectively have I and Q signals, which are mutually orthogonal. Since the desired signal to be received is positioned symmetrical with respect to the image signal mainly at a frequency of a frequency-divided signal “g” (local signal) on a frequency axis, the respective I signals of the desired signal to be received and the image signal are in phase, while the respective Q signals of the desired signal to be received and the image signal are in reverse phase.

[0158] Then, when the Q signal is allowed to undergo a 90-degree phase shift, as illustrated in FIG. 20B, the respective Q signals of the desired signal to be received and the image signal undergo a 90-degree phase shift, the I and Q signals of the desired signal to be received are in phase, while those of the image signal are in reverse phase. Therefore, synthesis of the phase-shifted I and Q signals will result in cancellation of an image signal component to take out only a desired signal component to be received.

[0159] Concretely, in the basic circuit 624F, the mixers 6245a and 6245b use signals (signals “g” and “g_i”) in which input signals are mutually orthogonal to effect frequency conversion, thereby to generate I and Q signals (signal “f_1I” and “f_1Q”) . Then, the generated I and Q signals are phase-shifted by the phase-shift circuits 6246a and 6246b (signals “f_2I” and “f_2Q”), and added/subtracted by the adder-subtractor 6247, thereby removing an image signal and outputting only a desired signal to be received.

[0160] As described above, according to Embodiment 5, each of the basic circuits 624F is constituted in such a way that each signal obtained by subjecting the respective input signals of I and Q signals to frequency conversion by using a signal “g” is phase-shifted to give a 90-degree phase-shift difference, added and synthesized, thereby to make it possible to remove an image signal component resulting from the frequency conversion.

[0161] In other words, the serially-connected basic circuit 624F multiplies an input signal by a signal “g” input from the frequency divider circuit 625 and a signal obtained by subjecting the signal “g” to a 90-degree phase shift, allows the multiplied signals to undergo a phase shift so as to give a 90-degree phase-shift difference with respect to each of the multiplied signals, and adds and subtracts them to output as a conversion signal. Thereby, I and Q signals obtained by subjecting the input signal to frequency conversion are phase-shifted so as to respectively give a 90-degree phase-shift difference, added and subtracted, thereby to make it possible to remove an image signal component resulting from the frequency conversion.

[0162] Other embodiments may also be available, which are combinations of Embodiments 1 to 4 described above.

[Function and Effect]

[0163] As described above, according to the radio wave timepiece 1 in the present embodiment, each of serially connected basic circuits 624 in a multi-stage frequency conversion circuit 623 makes synthesis by multiplying received signals received at a receiving antenna 621 by a signal “g” obtained by dividing a reference frequency signal bs at a predetermined frequency dividing ratio, thereby gradually decreasing the frequency. Then, in a detection circuit 626, detection is performed on the basis of a signal “a”, the frequency of which is decreased, thereby to output a detected signal “d”. Herein, since an oscillating signal for a timepiece generated by an oscillating circuit section 900 is used as a reference frequency signal bs, a local oscillating circuit, which was required in a conventional radio wave receiving apparatus based on super-heterodyne system, is no longer necessary. More specifically, since no PLL circuit is required, signals are received in a highly stable manner, which is free of any power-supply variation or variation in frequency resulting from ON/OFF operation at a power source, and an electric power consumed as a whole system can be decreased. Further, a multi-stage frequency conversion in which synthesis is made by multiplying received signals by the frequency-divided signal “g” to attain a gradual decrease in frequency makes it possible to receive signals at a high accuracy. In addition, each of the basic circuits 624 may be constituted with simple circuit elements, thereby to make it possible to provide a large-scale integration and reduce the dimension of chips, although the circuits are provided in a multiple stage and accordingly made larger in size.

[0164] Additionally, an embodiment in which the present invention is applicable is not limited to the embodiments described above but may be changed appropriately within a scope not deviating from an object of the present invention.

[0165] In the embodiments described above, the detection circuit 626 performs detection on the basis of a signal “a” output from the multi-stage frequency conversion circuit 623 to output a detected signal “d”. However, a final stage of the basic circuit 624 in the multi-stage frequency conversion circuit 623 may also act as the detection circuit 626.

[0166] FIG. 16 is a block diagram illustrating a constitution of a radio wave receiving apparatus 623E in this case. According to the figure, the radio wave receiving apparatus 623E is different in constitution from the radio wave receiving apparatus 623 shown in FIG. 2 in that it is provided with the multi-stage frequency conversion circuit 623E including serially connected n-stages of basic circuits 624[1], 624[2], . . . , 624[N] and 624[n+1] but not provided with the detection circuit 626.

[0167] A signal “a” from the previous stage of the basic circuit 624[N] and a signal “f” obtained by dividing a reference frequency signal bs from the frequency divider circuit 625 by a predetermined frequency dividing ratio, which is identical in frequency with the signal “a”, are respectively input into the final stage of the basic circuit 624[n+1] in the multi-stage frequency conversion circuit 623. Then, the basic circuit 624[n+1] outputs the signal “a” and a signal d, which is a difference frequency signal of the signal “f”. Since the signal “a” and the signal “f” are identical in frequency, the signal “d” is of 0 Hz. In other words, the output signal “d” from the multi-stage frequency conversion circuit 623 is a detected signal which has detected the signal “a”, namely, a signal which has regenerated a received signal.

[0168] Further, the radio wave receiving apparatus 620 may be constituted as illustrated in FIG. 21, which is a constitution in which the detection circuit 626 is included in the multi-stage frequency conversion circuit 623.

[0169] FIG. 21 is a block diagram illustrating a constitution of a radio wave receiving apparatus 620G in this case. The radio wave receiving apparatus 620G is to remove an image signal according to the same principle of Embodiment 5 described above, and constituted with a receiving antenna 621, a RF amplifier circuit 622, a multi-stage frequency conversion circuit 626G, a frequency divider circuit 625G, an AGC circuit 627 and a switch group 628G. Additionally, an explanation will be omitted for a block of functions and constitutions which is similar to that explained in FIG. 2.

[0170] The frequency divider circuit 625G divides a reference frequency signal bs input from a transmitting circuit section 900 by the respective frequency dividing ratios of 2, 1, 1/2, 1/4, . . . , 1/2^(m−2) (m is an integral number) and outputs the divided signals g1, g2, g3, . . . , gm respectively at output terminals of t1, t2, t3, . . . , tm.

[0171] The switch group 628G includes a plurality of switches S1 to S3 provided between a multi-stage frequency conversion circuit 629G and a frequency divider circuit 625G. These switches S1 to S3 are respectively connected to any one of output terminals t1, t2, . . . , tm of the frequency divider circuit 625G, for example, in accordance with a selected signal ss input from a CPU 100. Then, signals “g” output to the output terminals t connected to the respective switches S1 to S3 are input into the multi-stage frequency conversion circuit 629G as signals k1 to k3.

[0172] The multi-stage frequency conversion circuit 629G converts input signals from the RF amplifier circuit 622 into those having gradually lower frequencies on the basis of signals k1 to k3 input via the switch group 628G from the frequency divider circuit 625G and outputs them as signals “d”.

[0173] FIG. 22 is a view illustrating a circuit configuration of the multi-stage frequency conversion circuit 626G. According to the figure, the multi-stage frequency conversion circuit 629G is constituted with phase shifters 6291a to 6291c, mixers 6292a to 6262_l, filters 6293a to 6293h, adders-subtractors 6294a to 6294d and an adder 6295.

[0174] The mixer 6292a makes synthesis by multiplying a signal input into the multi-stage frequency conversion circuit 629G by a signal k1 to output them as a signal f_a1I. The filter 6293a is an LPF, allowing frequencies in a low frequency range including a difference frequency between the input signal and the signal k1 to pass through with respect to the signal f_a1I input from the mixer 6292a to output them, while cutting off frequency components beyond the range including a sum frequency.

[0175] The phase shifter 6291a allows the input signal k1 to undergo a 90-degree phase shift and outputs it as a signal k4. The mixer 6292b makes synthesis by multiplying the input signal by the signal k4 input from the phase shifter 6291a, thereby to output them as a signal f_a1Q. The filter 6293b is a LPF, allowing frequencies in a low frequency range including a difference frequency between the input signal and the signal k1 to pass through with respect to the signal f_a1Q input from the mixer 6292b to output them, while cutting off frequency components beyond the range including a sum frequency.

[0176] The mixer 6292c makes synthesis by multiplying a signal f_a1I input via the filter 6293a from the mixer 6292a by a signal k2 to output them as a signal f_b1I. The filter 6293a is a LPF, allowing frequencies in a low frequency range including a difference frequency between the signal f_a1I and the signal k2 to pass through with respect to the signal f_b1I input from the mixer 6292c to output them, while cutting off frequency components beyond the range including a sum frequency.

[0177] The phase shifter 6291b allows the input signal k2 to undergo a 90-degree phase shift and outputs it as a signal k5. The mixer 6292d makes synthesis by multiplying the signal f_a1I input via the filter 6293a from the mixer 6292a by the signal k5 input from the phase shifter 6291b to output them as a signal f_b1Q. The filter 6293d is a LPF, allowing frequencies in a low frequency range including a difference frequency between the signal f_a1I input from the mixer 6292d and the signal k2 to pass through with respect to the signal f_b1Q input from the mixer 6292d to output them, while cutting off frequency components beyond the range including a sum frequency.

[0178] The mixer 6292e makes synthesis by multiplying the signal f_a1Q input via the filter 6293b from the mixer 6292b by the signal k2 to output them as a signal “f_b2I”. The filter 6293e is a LPF, allowing frequencies in a low frequency range including a difference frequency between the signal “f_a1Q” and the signal k2 to pass through with respect to the signal f_b2I input from the mixer 6292e to output them, while cutting off frequency components beyond the range including a sum frequency.

[0179] The mixer 6292f makes synthesis by multiplying the signal f_a1Q input via the filter 6293b from the mixer 6292b by the signal k5 input from the phase shifter 6291b to output them as a signal f_b2Q. The filter 6293f is a LPF, allowing frequencies in a low frequency range including a difference frequency between the signal f_a1Q and the signal k2 to pass through with respect to the signal f_b2Q input from the mixer 6292f to output them, while cutting off frequency components beyond the range including a sum frequency.

[0180] The adder-subtractor 6294a makes synthesis by adding or subtracting a signal f_b1I input via the filter 6293c from the mixer 6292c to and from a signal f_b2Q input via the filter 6293f from the mixer 6292f, thereby to output them in accordance with a sum/difference switching signal 1 (wsk 1) to be input. The sum/difference switching signal 1 (wsk 1) is a signal for specifying operational contents (addition/subtraction) of the adder-subtractor 6294a and input, for example, from a CPU 100. Then, the adder-subtractor 6294a makes synthesis by adding the signal f_b1I to the signal f_b2Q, thereby to output them as a signal f_d, where “addition” is specified by the sum/difference switching signal 1 (wsk 1), and makes synthesis by subtracting the signal f_b1I from the signal f_b2Q, thereby to output them as a signal f_c, where “subtraction” is specified.

[0181] The adder-subtractor 6294b makes synthesis by adding or subtracting a signal f_b1Q input via the filter 6293d from the mixer 6292d to and from a signal f_b2I input via the filter 6293e from the mixer 6292e in accordance with a sum/difference switching signal 2 (wsk 2) to be input, thereby to output them. The sum/difference switching signal 2 (wsk 2) is a signal for specifying operational contents of the adder-subtractor 6294b and input, for example, from a CPU 100. The adder-subtractor 6294b makes synthesis by adding the signal f_b1Q to the signal f_b2I thereby to output them as a signal f_g, where “addition” is specified by the sum/difference switching signal 2 (wsk 2), and makes synthesis by subtracting the signal f_b1Q from the signal f_b2I, thereby to output them as a signal f_e, where “subtraction” is specified.

[0182] The mixer 6292g makes synthesis by multiplying a signal input from the adder-subtractor 6294a by a signal k3 to output them. More specifically, where a signal f_c is input from the adder-subtractor 6294a, it makes synthesis by multiplying the signal f_c by the signal k3 to output them as a signal f_cI3, and where a signal f_d is input, it makes synthesis by multiplying the signal f_d by the signal k3 to output them as a signal f_dI3.

[0183] The phase shifter 6291c allows the input signal k3 to undergo a 90-degree phase shift and outputs it as a signal k6. The mixer 6292h makes synthesis by multiplying a signal input from the adder-subtractor 6294b by the signal k6 input from the phase shifter 6291c to output them. More specifically, where a signal f_e is input from the adder-subtractor 6294b, it makes synthesis by multiplying the signal f_e by the signal k6 to output them as a signal f_eQ3, and where a signal f_g is input, it makes synthesis by multiplying the signal f_g by the signal k6 to output them as a signal f_gQ3.

[0184] The mixer 6292i makes synthesis by multiplying a signal input from the adder-subtractor 6294b by a signal k3 to output them. More specifically, where a signal f_e is input from the adder-subtractor 6294b, it makes synthesis by multiplying the signal f_e by the signal k3 to output them as a signal f_eI3, and where a signal f_g is input, it makes synthesis by multiplying the signal f_g by the signal k3 to output them as a signal f_gI3.

[0185] The mixer 6292j makes synthesis by multiplying a signal input from the adder-subtractor 6294a by a signal k6 input from the phase shifter 6291c to output them. More specifically, where a signal f_c is input from the adder-subtractor 6294a, it makes synthesis by multiplying the signal f_c by the signal k6 to output them as a signal f_eQ3, and where a signal f_d is input, it makes synthesis by multiplying the signal f_d by the signal k6 to output them as a signal f_dQ3.

[0186] The adder-subtractor 6294c makes synthesis by adding or subtracting signals input respectively from the mixers 6292g and 6292h in accordance with a sum/difference switching signal 3 (wsk 3) to be input, thereby to output them. The sum/difference switching signal 3 (wsk 3) is a signal for specifying operational contents of the adder-subtractor 6294c and input, for example, from a CPU 100. The adder-subtractor 6294c makes synthesis by adding a signal input from the mixer 6292g (signal f_cI3 or signal f_dI3) to a signal input from the mixer 6292h (signal f_eQ3 or signal f_gQ3), thereby to output them as a signal f_h, where “addition” is specified by the sum/difference switching signal 3 (wsk 3), and makes synthesis by subtracting a signal input from the mixer 6292g (signal f_cI3 or signal f_dI3) from a signal input from the mixer 6292h (signal f_eQ3 or signal f_gQ3), thereby to output them as a signal f_h where “subtraction” is specified.

[0187] The filter circuit 6293g is a LPF, allowing frequencies in a low frequency range including a difference frequency between signals output respectively from the mixers 6292g and 6292h to pass through with respect to a signal f_h input from the adder-subtractor 6294c to output them, while cutting off frequency components beyond the range including a sum frequency.

[0188] The adder-subtractor 6294d makes synthesis by adding or subtracting signals input respectively from the mixers 6292i and 6292j in accordance with a sum/difference switching signal 4 (wsk 4) to be input, thereby to output them. The sum/difference switching signal 4 (wsk 4) is a signal for specifying operational contents of the adder-subtractor 6294d and input, for example, from a-CPU 100. The adder-subtractor 6294d makes synthesis by adding signal input from the mixer 6292i (signal f_eI3 or signal f_gI3) to a signal input from the mixer 6292j (signal f_cQ3 or signal f_dQ3), thereby to output them as a signal f_i, where addition is specified by the sum/difference switching signal 4 (wsk 4), and makes synthesis by subtracting a signal input from the mixer 6292i (signal f_eI3 or signal f_gI3) from a signal input from the mixer 6292j (signal f_cQ3 or signal f_dQ3), thereby to output them as a signal f_i, where “subtraction” is specified.

[0189] The filter circuit 6293h is a LPF, allowing frequencies in a low frequency range including a difference frequency between signals output respectively from the mixers 6292i and 6292j to pass through with respect to a signal f_i input from the adder-subtractor 6294d to output them, while cutting off frequency components beyond the range including a sum frequency.

[0190] The mixer 6292k squares a signal f_h input via the filter 6293g from the adder-subtractor 6294c to output it. The mixer 6292l squares a signal f_i input via the filter 6293h from the adder-subtractor 6294d to output it. The adder 6295 makes synthesis by adding signals input respectively from the mixers 6292k and 6292l, thereby to output them. A signal output from the adder 6295 is given as an output signal d of the multi-stage frequency conversion circuit 629G.

[0191] Next, an explanation will be made for a specific operation of the multi-stage frequency conversion circuit 629G. First, an assumption is made that a signal f (ω) input to the multi-stage frequency conversion circuit 629G is expressed by the following equation (4a) and a signal f′(ω) obtained by allowing the input signal to undergo a 90-degree phase shift is expressed by the following equation (4b). $\begin{array}{cc}\begin{array}{c}f\left(\omega \right)=\cos \omega t\\ =\left(e^{\mathrm{j\omega }t}+e^{-\mathrm{j\omega }t}\right)/2\end{array}& \left(4a\right)\\ \begin{array}{c}{f}^{\prime }\left(\omega \right)=\sin \omega t\\ =\left(e^{\mathrm{j\omega }t}+e^{-\mathrm{j\omega }t}\right)/2j\end{array}& \left(4b\right)\end{array}$

[0192] An additional assumption is made that signals k1 to k3 are expressed respectively by the following equations (5a) to (5c), and signals k4 to k6 obtained by allowing these signals k1 to k3 to respectively undergo a 90-degree phase shift are expressed by the following equations (6a) to (6c). $\begin{array}{cc}\begin{array}{c}k1=\cos \omega 1t\\ =\left(e^{\mathrm{j\omega 1}t}+e^{-\mathrm{j\omega }1t}\right)/2\end{array}& \left(5a\right)\\ \begin{array}{c}k2=\cos \mathrm{\omega 2t}\\ =\left(e^{\mathrm{j\omega 2}t}+e^{-\mathrm{j\omega }2t}\right)/2\end{array}& \left(5b\right)\\ \begin{array}{c}k3=\cos \mathrm{\omega 3}t\\ =\left(e^{\mathrm{j\omega 3}t}+e^{-\mathrm{j\omega }3t}\right)/2\end{array}& \left(5c\right)\\ \begin{array}{c}k4=\sin \mathrm{\omega 1}t\\ =\left(e^{\mathrm{j\omega 1}t}-e^{-\mathrm{j\omega }1t}\right)/2j\end{array}& \left(6a\right)\\ \begin{array}{c}k5=\sin \mathrm{\omega 2}t\\ =\left(e^{\mathrm{j\omega 2}t}-e^{-\mathrm{j\omega }2t}\right)/2j\end{array}& \left(6b\right)\\ \begin{array}{c}k6=\sin \mathrm{\omega 3}t\\ =\left(e^{\mathrm{j\omega 3}t}-e^{-\mathrm{j\omega }3t}\right)/2j\end{array}& \left(6c\right)\end{array}$

[0193] In the multi-stage frequency conversion circuit 629G, first, the mixers 6292a and 6292b perform a first-stage frequency conversion with respect to an input signal f (ω). Namely, the input signal f (ω) is allowed to undergo frequency conversion with a signal k1 by using the mixer 6292a, thereby generating a signal f_a1I. The signal f_a1I is expressed by the following equation (7). $\begin{array}{cc}\begin{array}{c}{f}_{a1I}=\left(1/4\right)\left(e^{\mathrm{j\omega }t}+e^{-\mathrm{j\omega }t}\right)\left(e^{\mathrm{j\omega 1}t}+e^{-\mathrm{j\omega 1}t}\right)\\ =\left(1/4\right)\left(e^{j\left(\omega +\omega 1\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}\right)t}+e^{j\left(\omega -\omega 1\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)\\ =1/2\left(1/2\right)·\left\{\begin{array}{c}\left(e^{j\left(\omega +\omega 1\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)+\\ \left(e^{j\left(\omega -\omega 1\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)\end{array}\right\}\\ =f\left(\omega +\omega 1\right)+f\left(\omega -\omega 1\right)\end{array}& \left(7\right)\end{array}$

[0194] Further, the input signal f (ω) is allowed to undergo frequency conversion with a signal k4 by using the mixer 6292b, thereby generating a signal f_a1Q. The signal f_a1Q is expressed by the following equation (8). $\begin{array}{cc}\begin{array}{c}{f}_{a1Q}=\left(1/4j\right)\left(e^{\mathrm{j\omega }t}+e^{-\mathrm{j\omega }t}\right)\left(e^{\mathrm{j\omega 1}t}-e^{-\mathrm{j\omega 1}t}\right)\\ =\left(1/4j\right)\left(e^{j\left(\omega +\omega 1\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}\right)t}-e^{j\left(\omega -\omega 1\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)\\ =1/2\left(1/2j\right)·\left\{\begin{array}{c}\left(e^{j\left(\omega +\omega 1\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)-\\ \left(e^{j\left(\omega -\omega 1\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)\end{array}\right\}\\ =f\left(\omega +\omega 1-\pi /2\right)-f\left(\omega -\omega 1-\pi /2\right)\end{array}& \left(8\right)\end{array}$

[0195] Therefore, according to the equations (7) and (8), the first-stage frequency conversion generates two signals having the respective frequencies of “ω+ω1” and “ω−ω1.” FIG. 23A and FIG. 23B are views illustrating concepts of the relationship of two signals generated by the first-stage frequency conversion. FIG. 23A is a view illustrating a phase relationship, and FIG. 23B is a view illustrating a frequency relationship. The signal having a frequency of “ω−ω1” indicated by the solid line is a desired signal to be received, and the signal having a frequency of “ω+ω1” indicated by the dotted line is an image signal.

[0196] FIG. 23A is a view illustrating a phase relationship between the signal f_a1I and the signal f_a1Q on the same frequency axis. As illustrated in FIG. 23A, the signal f_a1I is orthogonal with the signal f_a1Q. Further, signals f_a1I are the respective I signals of an desired signal to be received and an image signal, which are in phase. Signals f_a1Q are the respective Q signal of a desired signal to be received and an image signal, which are mutually in reverse phase. Further, as illustrated in FIG. 23B, a desired signal to be received is positioned symmetrical with respect to an image signal mainly at a frequency ω1 of signal k1 on a frequency axis.

[0197] Then, the mixers 6292c to 6292f perform a second-stage frequency conversion. Namely, the input signal f_a1I is allowed to undergo frequency conversion with a signal k2 by using the mixer 6292c, thereby generating a signal f_b1I. The signal f_b1I is expressed by the following equation (9). $\begin{array}{cc}\begin{array}{c}{f}_{b1I}=[1/2\left(1/2\right)·\{\left(e^{j\left(\omega +\omega 1\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)+\\ \left(e^{j\left(\omega -\omega 1\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)·\left(e^{\mathrm{j\omega 2}t}+e^{-\mathrm{j\omega }2t}\right)/2\\ =1/4\{\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)\}/2\\ =\left(1/4\right)\{f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)+f\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)+\\ f\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)+f\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)\}\end{array}& \left(9\right)\end{array}$

[0198] Further, the signal f_a1I is allowed to undergo frequency conversion with a signal k5 by using the mixer 6292d, thereby generating a signal f_b1Q. The signal f_b1Q is expressed by the following equation (10). $\begin{array}{cc}\begin{array}{c}{f}_{b1Q}=[1/2\left(1/2\right)·\{\left(e^{j\left(\omega +\omega 1\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)+\\ \left(e^{j\left(\omega -\omega 1\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)·\left(e^{\mathrm{j\omega 2}t}-e^{-\mathrm{j\omega }2t}\right)/2j\\ =\left(1/4\right)\{\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)\}/2j\\ =\left(1/4\right)\{f^{\prime }\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)-f^{\prime }\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)+\\ f^{\prime }\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)-f^{\prime }\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)\}\end{array}& \left(10\right)\end{array}$

[0199] Still further, the signal f_a1Q is allowed to undergo frequency conversion with a signal k2 by using the mixer 6292e, thereby generating a signal f_b2I. The signal f_b2I is expressed by the following equation (11). $\begin{array}{cc}\begin{array}{c}{f}_{b2I}=[1/2\left(1/2j\right)·\{\left(e^{j\left(\omega +\omega 1\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)-\\ \left(e^{j\left(\omega -\omega 1\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)\}·\left(e^{\mathrm{j\omega 2}t}+e^{-\mathrm{j\omega }2t}\right)/2\\ =1/4\{\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)\}/2j\\ =\left(1/4\right)\{f^{\prime }\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)+f^{\prime }\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)-\\ f^{\prime }\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)-f^{\prime }\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)\}\end{array}& \left(11\right)\end{array}$

[0200] In addition, the signal f_a1Q is allowed to undergo frequency conversion with a signal k5 by using the mixer 6292f, thereby generating a signal f_b2Q. The signal f_b2Q is expressed by the following equation (12). $\begin{array}{cc}\begin{array}{c}{f}_{\mathrm{b2Q}}=1/2\left(1/2j\right)·\left\{\begin{array}{c}\left(e^{j\left(\omega +\mathrm{\omega 1}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}\right)t}\right)-\\ \left(e^{j\left(\omega -\mathrm{\omega 1}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}\right)t}\right)\end{array}\right\}·\\ \left(e^{\mathrm{j\omega 2}t}-e^{-\mathrm{j\omega 2}t}\right)/2j\\ =-\left(\frac{1}{4}\right)\left\{\begin{array}{c}\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)\end{array}\right\}/2\\ =\left(\frac{1}{4}\right)\left\{\begin{array}{c}-f\left(\omega +\omega 1+\mathrm{\omega 2}\right)+f\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)+\\ f\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)-f\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)\end{array}\right\}\end{array}& \left(12\right)\end{array}$

[0201] Herein, according to the equations (9) to (12), the second-stage frequency conversion generates four signals having the respective frequencies of “ω+ω1+ω2,” “ω+ω1−ω2,” “ω−ω1+ω2” and “ω−ω1−ω2.”

[0202] FIG. 24A to FIG. 24B and FIG. 25 are views illustrating concepts of relationship of signals generated by the second-stage frequency conversion. In FIG. 24A to FIG. 24B and FIG. 25, a desired signal of the frequency “ω−ω1−ω2” indicated by the solid line is a desired signal to be received, and signals having frequencies, “ω+ω1+ω2,” “ω−ω1+ω2” and “ω+ω1−ω2,” indicated by the dotted line, one-dot chain line and two-dot chain line are respectively image signals 1 to 3.

[0203] FIG. 24A to FIG. 24B are views illustrating phase-shift relationships of individual signals. FIG. 24A is a view illustrating a phase relationship between the signal f_b1I and the signal f_b1Q on the same frequency axis. FIG. 24B is a view illustrating a phase relationship between the signal f_b2I and the signal f_b2Q on the same frequency axis. As illustrated in FIG. 24A to FIG. 24B, the signal f_b1I is orthogonal to the signal f_b1Q, and the signal f_b2I is orthogonal to the signal f_b2Q.

[0204] Further, FIG. 25 is a view illustrating the frequency relationship of individual signals. As illustrated in the view, an image signal 1 of frequency “ω+ω1+ω2” is positioned symmetrical with respect to a signal to be received mainly at a frequency ω1 of signal k1, an image signal 2 of frequency “ω−ω1+ω2” is positioned symmetrical with respect to a desired image to be received mainly at a frequency ω2 of signal k2, and an image signal 3 of frequency “ω+ω1−ω2” is positioned symmetrical with respect to the image signal 1 mainly at a frequency ω2_i positioned symmetrical with respect to the signal ω₂ mainly at a frequency ω₁.

[0205] Next, according the equations (9) through (12) and FIG. 24A through FIG. 24B, signals of individual frequencies can be taken out as follows. First, a signal f (ω−ω1−ω2) of frequency “ω−ω1−ω2” can be taken out as follows. Namely, a signal f_b2Q is subtracted from a signal f_b1I. Further, a signal f_b1Q is added to a signal f_b2I and the phase is allowed to delay by 90 degrees. Then, these two signals are added to cancel signal components of other frequencies. Therefore, the signal f (ω−ω1−ω2) can be expressed by the following equation (13).
f(ω−ω1−ω2)=f_b1I−f_b2Q+P(f_b1Q+f_b2I)   (13)

[0206] Additionally, in the above equation (13), the function P (f) is a function which allows a phase of the signal “f” to delay by 90 degrees.

[0207] Further, a signal f (ω+ω1+ω2) of frequency “ω+ω1+ω2” can be taken out as follows. Namely, a signal f_b2Q is subtracted from a signal f_b1I. Further, a signal f_b1Q is added to a signal f_b2Q and the phase is allowed to advance by 90 degrees. Then, these two signals are added to cancel signal components of other frequencies. Therefore, the signal f (ω+ω1+ω2) can be expressed by the following equation (14).
f(ω+ω1+ω2)=f_b1I−f_b2Q−P(f_b1Q+f_b2I)   (14)

[0208] Still further, a signal f (ω−ω1+ω2) of frequency “ω−ω1+107 2” can be taken out as follows. Namely, a signal f_b1I is added to a signal f_b2Q. Further, a signal f_b2I is subtracted from a signal f_b1Q and the phase is allowed to advance by 90 degrees. Then, these two signals are added to cancel signal components of other frequencies. Therefore, the signal f (ω−ω1+ω2) can be expressed by the following equation (15). $\begin{array}{cc}\begin{array}{c}f(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}=f_{b1I}+f_{b2Q}+P\left(-f_{b1Q}+f_{b2I}\right)\\ =f_{b1I}+f_{b2Q}-P\left(f_{b1Q}-f_{b2I}\right)\end{array}& \left(15\right)\end{array}$

[0209] In addition, a signal f (ω+ω1−ω2) of frequency “ω+ω1−ω2” can be taken out as follows. Namely, a signal f_b1I is added to a signal f_b2Q. Further, a signal f_b2I is subtracted from a signal f_b1Q and the phase is allowed to delay by 90 degrees. Then, these two signals are added to cancel signal components of other frequencies. Therefore, the signal f (ω+ω1−ω2) can be expressed by the following equation (16).
f(ω+ω1−ω2)=f_b1I+f_b2Q+P(f_b1Q−f_b2I)   (16)

[0210] These equations (13) through (16) can decide the respective operational contents (addition/subtraction) of adders-subtractors 6294a to 6294d as illustrated in FIG. 26. Namely, the addition/subtraction by the respective first halves of the equations (13) to (16) can decide operational contents of the adder-subtractor 6294a, while the addition/subtraction by the respective latter halves can decide operational contents of the adder-subtractor 6294b. Further, the respective 90-degree phase shifts (advance/delay) of the equations (13) to (16) as well as the addition/subtraction by the first halves and the latter halves can decide the respective operational contents of the adders-subtractors 6294c and 6294d.

[0211] Next, according to the table in FIG. 26, the adder-subtractor 6294a generates a signal f_d by making synthesis by adding a signal f_b1I to a signal f_b2Q or a signal f_c by making synthesis by subtracting a signal f_b2Q from a signal f_b1I. The signal f_d is expressed by the following equation (17), and the signal f_c is expressed by the following equation (18). $\begin{array}{cc}\begin{array}{c}{f}_d=f_{b1I}+f_{b2Q}\\ =\left(1/2\right)\left\{\begin{array}{c}\left(e^{j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)}+e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)\end{array}\right\}/2\end{array}& \left(17\right)\\ \begin{array}{c}{f}_c=f_{b1I}-f_{b2Q}\\ =\left(1/2\right)\left\{\begin{array}{c}\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)\end{array}\right\}/2\end{array}& \left(18\right)\end{array}$

[0212] Further, the adder-subtractor 6294b generates a signal f_g by making synthesis by adding a signal f_b1Q to a signal f_b2I or a signal f_e by making synthesis by subtracting a signal f_b2I from a signal f_b1Q. The signal f_g is expressed by the following equation (19), and the signal f_e is expressed by the following equation (20). $\begin{array}{cc}\begin{array}{c}{f}_g=f_{b1Q}+f_{b2I}\\ =\left(1/2\right)\left\{\begin{array}{c}\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)-\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)\end{array}\right\}/2j\end{array}& \left(19\right)\\ \begin{array}{c}{f}_e=f_{b1Q}-f_{b2I}\\ =\left(1/2\right)\left\{\begin{array}{c}\left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}-e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}-e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}\right)t}\right)\end{array}\right\}/2j\end{array}& \left(20\right)\end{array}$

[0213] Next, mixers 6292g to 6292j perform a third-stage frequency conversion. Namely, the mixer 6292g generates a signal f_cI3 by allowing a signal f_c to undergo frequency conversion with a signal k3 or a signal f_dI3 by allowing a signal f_d to undergo frequency conversion with a signal k3. The signal f_cI3 is expressed by the following equation (21), and signal f_dI3 is expressed by the following equation (22). $\begin{array}{cc}\begin{array}{c}{f}_{\mathrm{cI}3}=\left(f_{b1I}-f_{b2Q}\right)·\left(e^{\mathrm{j\omega 3}t}+e^{-\mathrm{j\omega 3}t}\right)/2\\ =\{\left(e^{j\left(\omega +\omega 1+\omega 2+\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\omega 1-\omega 2-\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}+\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}\right)/8\\ =\left(1/4\right)\{f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)+f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)+\\ f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)+f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)+\\ f\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}+\mathrm{\omega 3}\right)+f\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)\}\end{array}& \left(21\right)\\ \begin{array}{c}{f}_{\mathrm{dI}3}=\left(f_{b1I}+f_{b2Q}\right)·\left(e^{\mathrm{j\omega 3}t}+e^{-\mathrm{j\omega 3}t}\right)/2\\ =\{\left(e^{j\left(\omega +\omega 1-\omega 2+\mathrm{\omega 3}\right)t}+e^{-j\left(\omega +\omega 1-\omega 2-\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}+\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)t}\right)/8\\ =\left(1/4\right)\{f\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}+\mathrm{\omega 3}\right)+f\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)+\\ f\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)+f\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)\}\end{array}& \left(22\right)\end{array}$

[0214] Further, the mixer 6292h generates a signal f_eQ3 by allowing a signal f_e to undergo frequency conversion with a signal k6 or a signal f_gQ3 by allowing a signal f_g to undergo frequency conversion with a signal k6. The signal f_eQ3 is expressed by the following equation (20), and signal f_gQ3 is expressed by the following equation (24). $\begin{array}{cc}\begin{array}{c}{f}_{eQ3}=\left(f_{b1Q}-f_{b2I}\right)·\left(e^{\mathrm{j\omega 3}t}-e^{-\mathrm{j\omega 3}t}\right)/2j\\ =-\{\left(e^{j\left(\omega +\omega 1-\omega 2+\mathrm{\omega 3}\right)t}-e^{-j\left(\omega +\omega 1-\omega 2-\mathrm{\omega 3}\right)t}\right)+\\ \left(e^{j\left(\omega -\omega 1+\omega 2+\mathrm{\omega 3}\right)t}-e^{-j\left(\omega -\omega 1+\omega 2-\mathrm{\omega 3}\right)t}\right)+\\ \left(-e^{j\left(\omega +\omega 1-\omega 2+\mathrm{\omega 3}\right)t}+e^{-j\left(\omega +\omega 1-\omega 2-\mathrm{\omega 3}\right)t}\right)+\\ \left(-e^{j\left(\omega -\omega 1+\omega 2-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\omega 1+\omega 2+\mathrm{\omega 3}\right)t}\right)/8\\ =\left(1/4\right)\{-f\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}+\mathrm{\omega 3}\right)+\\ f\left(\omega +\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)-f\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)+\\ f\left(\omega -\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)\}\end{array}& \left(23\right)\\ \begin{array}{c}{f}_{gQ3}=\left(f_{b1Q}+f_{b2I}\right)·\left(e^{\mathrm{j\omega 3}t}-e^{-\mathrm{j\omega 3}t}\right)/2j\\ =-\{\left(e^{j\left(\omega +\omega 1+\omega 2+\mathrm{\omega 3}\right)t}-e^{-j\left(\omega +\omega 1+\omega 2-\mathrm{\omega 3}\right)t}\right)-\\ \left(e^{j\left(\omega -\omega 1-\omega 2+\mathrm{\omega 3}\right)t}-e^{-j\left(\omega -\omega 1-\omega 2-\mathrm{\omega 3}\right)t}\right)+\\ \left(-e^{j\left(\omega +\omega 1+\omega 2-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega +\omega 1+\omega 2+\mathrm{\omega 3}\right)t}\right)-\\ \left(-e^{j\left(\omega -\omega 1+\omega 2-\mathrm{\omega 3}\right)t}+e^{-j\left(\omega -\omega 1+\omega 2+\mathrm{\omega 3}\right)t}\right)/8\\ =\left(1/4\right)\{-f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}+\mathrm{\omega 3}\right)+\\ f\left(\omega +\mathrm{\omega 1}+\mathrm{\omega 2}-\mathrm{\omega 3}\right)+f\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}+\mathrm{\omega 3}\right)-\\ f\left(\omega -\mathrm{\omega 1}-\mathrm{\omega 2}-\mathrm{\omega 3}\right)\}\end{array}& \left(24\right)\end{array}$