Adaptive radio transceiver with a local oscillator

[0002] The present application is a continuation of co-pending patent application Ser. No. 09/634,552, filed Aug. 8, 2000, priority of which is hereby claimed under 35 U.S.C. §120. The present application also claims priority under 35 U.S.C. §119(e) to provisional Application Nos. 60/160,806, filed Oct. 21, 1999; Application No. 60/163,487, filed Nov. 4, 1999; Application No. 60/163,398, filed Nov. 4, 1999; Application No. 60/164,442, filed Nov. 9, 1999; Application No. 60/164,194, filed Nov. 9, 1999; Application No. 60/164,314, filed Nov. 9, 1999; Application No. 60/165,234, filed Nov. 11, 1999; Application No. 60/165,239, filed Nov. 11, 1999; Application No. 60/165,356; filed Nov. 12, 1999; Application No. 60/165,355, filed Nov. 12, 1999; Application No. 60/172,348, filed Dec. 16, 1999; Application No. 60/201,335, filed May 2, 2000; Application No. 60/201,157, filed May 2, 2000; Application No. 60/201,179, filed May 2, 2000; Application No. 60/202,997, filed May 10, 2000; Application No. 60/201,330, filed May 2, 2000. All these applications are expressly incorporated herein by referenced as though fully set forth in full.

[0003] The present invention relates to telecommunication systems, and in particular, to radio transceiver systems and techniques.

[0004] Transceivers are used in wireless communications to transmit and receive electromagnetic waves in free space. In general, a transceiver comprises three main components: a transmitter, a receiver, and an LO generator or frequency synthesizer. The function of the transmitter is to modulate, upconvert, and amplify signals for transmission into free space. The function of the receiver is to detect signals in the presence of noise and interference, and provide amplification, downconversion and demodulation of the detected the signal such that it can be displayed or used in a data processor. The LO generator provides a reference signal to both the transmitter for upconversion and the receiver for downconversion.

[0005] Transceivers have a wide variety of applications ranging from low data rate wireless applications (such as mouse and keyboard) to medium data rate Bluetooth and high data rate wireless LAN 802.11 standards. However, due to the high cost, size and power consumption of currently available transceivers, numerous applications are not being fully commercialized. A simplified architecture would make a transceiver more economically viable for wider applications and integration with other systems. The integration of the transceiver into a single integrated circuit (IC) would be an attractive approach. However, heretofore, the integration of the transceiver into a single IC has been difficult due to process variations and mismatches. Accordingly, there is a need for an innovative transceiver architecture that could be implemented on a single IC, or alternatively, with a minimum number of discrete off-chip components that compensate for process variations and mismatches.

[0006] In one aspect of the present invention, an oscillator circuit includes an oscillator to generate a first signal having a first frequency, a second oscillation source to generate a second signal having a second frequency, and a mixer to mix to the first and second signals.

[0007] In another aspect of the present invention, an oscillator circuit, comprising oscillation means for generating a first signal having a first frequency, signal generation means for generating a second signal having a second frequency, and mixer means for mixing the first and second signals.

[0008] In yet another aspect of the present invention, a transceiver includes a local oscillator generator having an oscillator with a first signal having a first frequency, a frequency divider coupled to the oscillator to divide the first frequency off the first signal to produce a second signal having a second frequency, the frequency divider having a programmable divisor, and a mixer to mix the first and second signals, and a controller to program the divisor.

[0009] In still another aspect of the present invention, a method of generating a signal having a signal frequency includes generating a first signal having a first frequency, dividing the first frequency to generate a second signal having a second frequency, and mixing the first and second signals to generate the signal frequency.

[0010] In a further aspect of the present invention, a method of generating a local oscillator having a signal frequency includes generating a first signal having a first frequency, generating a second signal having a second frequency, and mixing the first and second signals to generate the signal frequency.

[0011] It is understood that other embodiments of the present invention will become readily apparent to those skilled in the art from the following detailed description, wherein it is shown and described only embodiments of the invention by way of illustration of the best modes contemplated for carrying out the invention. As will be realized, the invention is capable of other and different embodiments and its several details are capable of modification in various other respects, all without departing from the spirit and scope of the present invention. Accordingly, the drawings and detailed description are to be regarded as illustrative in nature and not as restrictive.

[0012] These and other features, aspects, and advantages of the present invention will become better understood with regard to the following description, appended claims, and accompanying drawings where:

[0013] FIG. 1 is a block diagram of a transceiver in accordance with an exemplary embodiment of the present invention;

[0014] FIG. 2 is a block diagram of the transceiver blocks including a receiver, transmitter and local oscillator in accordance with an exemplary embodiment of the present invention;

[0015] FIG. 3 is a block diagram of a mixer in accordance with an exemplary embodiment of the present invention;

[0016] FIG. 4 is a block diagram of a local oscillator (LO) architecture in accordance with an exemplary embodiment of the present invention;

[0017] FIG. 5 is a block diagram of an LO architecture in accordance with another exemplary embodiment of the present invention;

[0018] FIG. 6 is a block diagram of a LO architecture in accordance with an alternative exemplary embodiment of the present invention;

[0019] FIG. 7 is a block diagram of a LO architecture in accordance with an yet another exemplary embodiment of the present invention;

[0020] FIG. 8 is a block diagram of a limiting buffer for the LO architecture of FIG. 33 in accordance with an exemplary embodiment of the present invention;

[0021] FIG. 9 is a block diagram of a wide tuning range voltage controlled oscillator (VCO) in accordance with an exemplary embodiment of the present invention;

[0022] FIG. 10 is an electrical diagram of the wide tuning range VCO of FIG. 34 in accordance with an exemplary embodiment of the present invention;

[0023] FIG. 11 is a graphical depiction showing a typical VCO tuning curve;

[0024] FIG. 12 is a graphical depiction of a segmented VCO tuning curve in accordance with an exemplary embodiment of the present invention;

[0025] FIG. 13 is a block diagram of a cross-coupled VCO in combination with a frequency divider in accordance with an exemplary embodiment of the present invention;

[0026] FIG. 14 is a block diagram of a VCO in combination with a divider and polyphase circuit in accordance with an exemplary embodiment of the present invention;

[0027] In accordance with an exemplary embodiment of the present invention, a tranceiver utilizes a combination of frequency planning, circuit design, layout and implementation, differential signal paths, dynamic calibration, and self-tuning to achieve robust performance over process variation and interference. This approach allows for the full integration of the transceiver onto a single IC for a low cost, low power, reliable and more compact solution. This can be achieved by (1) moving external bulky and expensive image reject filters, channel select filters, and baluns onto the RF chip; (2) reducing the number of off-chip passive elements such as capacitors, inductors, and resistors by moving them onto the chip; and (3) integrating all the remaining components onto the chip. As those skilled in the art will appreciate, the described exemplary embodiments of the transceiver do not require integration into a single IC and may be implemented in a variety of ways including discrete hardware components.

[0028] As shown in FIG. 1, a described exemplary embodiment of the transceiver includes an antenna 8, a switch 9, a receiver 10, a transmitter 12, a local oscillator (LO) generator (also called a synthesizer) 14, a controller 16, and a self-testing unit 18. All of these components can be packaged for integration into a single IC including components such as filters and inductors.

[0029] The transceiver can operate in either a transmit or receive mode. In the transmit mode, the transmitter 12 is coupled to the antenna 8 through the switch 9. The switch 9 provides sufficient isolation to prevent transmitter leakage from desensitizing or damaging the receiver 10. In the receive mode, the switch 9 directs signal transmissions from the antenna 8 to the receiver 10. The position of the switch 9.can be controlled by an external device (not shown) such as a computer or any other processing device known in the art.

[0030] The receiver 10 provides detection of desired signals in the presence of noise and interference. It should be able extract the desired signals and amplify it to a level where information contained in the received transmission can be processed. In the described exemplary embodiment, the receiver 10 is based on a heterodyne complex (I-Q) architecture with a programmable intermediate frequency (IF). The LO generator 14 provides a reference signal to the receiver 10 to downconvert the received transmission to the programmed IF.

[0031] A low IF heterodyne architecture is chosen over a direct conversion receiver because of the DC offset problem in direct conversion architectures. DC offset in direct conversion architectures arises from a number of sources including impedance mismatches, variations in threshold voltages due to process variations, and leakage from the LO generator to the receiver. With a low IF architecture, AC coupling between the IF stages can be used to remove the DC offset.

[0032] The transmitter 12 modulates incoming data onto a carrier frequency. The modulated carrier is upconverted by the reference signal from the LO generator 14 and amplified to a sufficient power level for radiation into free space through the antenna 8. The transmitter uses a direct conversion architecture. With this approach only one step of upconversion is required This leads to a reduction in both circuit complexity and power consumption.

[0033] The controller 16 performs two functions. The first function provides for adaptive programming of the receiver 10, transmitter 14 and LO generator 16. By way of example, the transceiver can be programmed to handle various communication standards for local area networks (LAN) and personal area networks (PAN) including HomeRF, IEEE 802.11, Bluetooth, or any other wireless standard known in the art. This entails programming the transceiver to handle different modulation schemes and data rates. The described exemplary embodiment of the transceiver can support modulation schemes such as Binary Phase Shift Keying (BPSK), Quadrature Phase Shift Keying (QPSK), offset quadrature phase shift keying (OQPSK), Multiple frequency modulations such as M level frequency shift keying (FSK), Continuous Phase Frequency Shift Keying modulation (CFSK), Minimum Shift Keying modulation (MSK), Gaussian filtered FSK modulation (GFSK), and Gaussian filtered Minimum Shift Keying (GMSK), Phase/Amplitude modulation (such as Quadrature Amplitude Modulation (QAM)), orthogonal frequency modulation (such as Orthogonal Frequency Division Multiplexing (OFDM)), direct sequence spread spectrum systems, and frequency hopped spread spectrum systems and numerous other modulation schemes known in the art. Dynamic programming of the transceiver can also be used to provide optimal operation in the presence of noise and interference. By way of example, the IF can be programmed to avoid interference from an external source.

[0034] The second function provides for adaptive calibration of the receiver 10, transmitter 14 and LO generator 16. The calibration functionality controls the parameters of the transceiver to account for process and temperature variations that impact performance. By way of example, resistors can be calibrated within exacting tolerances despite process variations in the chip fabrication process. These exacting tolerances can be maintained in the presence of temperature changes by adaptively fine tuning the calibration of the resistors.

[0035] The controller 16 can be controlled externally by a central processing unit (CPU), a microprocessor, a digital signal processor (DSP), a computer, or any other processing device known in the art. In the described exemplary embodiment, a control bus 17 provides two way communication between the controller 16 and the external processing device (not shown). This communication link can be used to externally program the transceiver parameters for different modulation schemes, data rates and IF operating frequencies. The output of the controller 16 is used to adjust the parameters of the transceiver to achieve optimal performance in the presence of process and temperature variations for the selected modulation scheme, data rate and IF.

[0036] The self-testing unit 18 generates test signals with different amplitudes and frequency ranges. The test signals are coupled to the receiver 10, transmitter 12 and LO generator 14 where they are processed and returned to the self-testing unit 18. The return signals are used to determine the gain, frequency characteristics, selectivity, noise floor, and distortion behavior of the receiver 10, transmitter 12 and LO generator 14. This is accomplished by measuring the strength of the signals output from the self-testing unit 18 against the returned signals over the tested frequency ranges. In an exemplary embodiment of the self-testing unit 18, these measurements can be made with different transceiver parameters by sweeping the output of the controller 16 through its entire calibrating digital range, or alternatively making measurements with the controller output set to a selected few points, by way of example, at the opposite ends of the digital range.

[0037] In the described exemplary embodiment, the self-testing unit 18 is in communication with the external processing device (not shown) via the control bus 17. During self-test, the external processing device provides programming data to both the controller 16 and the self-testing unit 18. The self-testing unit 18 utilizes the programming data used by the controller 16 to set the parameters of the transceiver to determine the gain, frequency characteristics, selectivity, noise floor, and distortion behavior of the receiver 10, transmitter 12 and LO generator 14.

[0038] FIG. 2 shows a block diagram of the transceiver in accordance with an embodiment of the invention. The described exemplary embodiment is integrated into a single IC. For ease of understanding, each component coupled to the controller is shown with a “program” designation or a “calibration” designation. These designations indicate whether the component is programmed by the controller or calibrated by the controller. In practice, in accordance with the described exemplary embodiment of the present invention, the components that are programmed receive the MSBs and the components that are calibrated receive the LSBs. The components requiring both programming and calibration receive the entire digital output from the controller. As those skilled in the art will appreciate, any number of methodologies may be used to deliver programming and calibration information to the individual components. By way of example, a single controller bus could be used having the programming and or calibration data with the appropriate component addresses.

[0039] The receiver 10 front end includes a low noise amplifier (LNA) 22 which provides high gain with good noise figure performance. Preferably, the gain of the LNA 22 can be set by the controller (not shown) through a “select gain” input to maximize the receivers dynamic range. The desirability of dynamic gain control arises from the effect of blockers or interferers which can desensitize the LNA. Conventional filter designs at the input of the LNA 22 may serve to sufficiently attenuate undesired signals below a certain power level, however, for higher power blockers or interferers, the LNA 22 should be operated with low gain.

[0040] The output of the LNA 22 is downconverted to a low IF frequency by the combination of complex IF mixers 24 and a complex bandpass filter 26. More particularly, the output of the LNA 22 is coupled to the complex IF mixers 24 which generate a spectrum of frequencies based upon the sum and difference of the received signal and the RF clocks from the LO generator. The complex bandpass filter passes the complex IF signal while rejecting the image of the received signal. The image rejection capability of the complex IF mixers 24 in cooperation with the complex bandpass filter 26 eliminates the need for the costly and power consuming preselect filter typically required at the input of the LNA for conventional low IF architectures.

[0041] The output of the complex bandpass filter 26 is coupled to a programmable multiple gain stage amplifier 28. The amplifier 28 can be designed to be programmable to select between a limiter and an automatic gain control (AGC) feature, depending on the modulation scheme used in the transceiver. The limiting amplifier can be selected if the transceiver uses a constant envelope modulation such as FSK. AGC can be selected if the modulation is not a constant envelope, such as QAM. In addition, the bandwidth of the amplifier 28 can be changed by the controller to accommodate various data rates and modulation schemes.

[0042] The output of the amplifier 28 is coupled to a second set of complex IF mixers 30 where it is mixed with the IF clocks from the LO generator for the purpose of downconverting the complex IF signal to baseband. The complex IF mixers 30 not only reject the image of the complex IF signal, but also reduces some of the unwanted cross modulation spurious signals thereby relaxing the filtering requirements.

[0043] The complex baseband signal from the mixers 30 is coupled to a programmable passive polyphase filter within a programmable low pass filter 32. The programmable low pass filter 32 further filters out higher order cross modulation products. The polyphase filter can be centered at four times the IF frequency to notch out one of the major cross modulation products which results from the multiplication of the third harmonic of the IF signal with the IF clock. After the complex baseband signal is filtered, it either is passed through an analog-to-digital (A/D) converter 34 to be digitized or is passed to an analog demodulator 36. The analog demodulator 36 can be implemented to handle any number of different modulation schemes by way of example FSK. Embodiments of the present invention with an FSK demodulator uses the A/D converter 36 to sample baseband data with other modulation schemes for digital demodulation in a digital signal processor (not shown).

[0044] The LO generator 14 provides the infrastructure for frequency planning. The LO generator 14 includes an IF clock generator 44 and an RF clock generator 47. The IF clock generator includes an oscillator 38 operating at a ratio of the RF signal (f_OCS). High stability and accuracy can be achieved in a number of ways including the use of a crystal oscillator.

[0045] The reference frequency output from the oscillator 38 is coupled to a divider 40. The divider 40 divides the reference signal f_OSCby a number L to generate the IF clocks for downconverting the complex IF signal in the receiver to baseband. A clock generator 41 is positioned at the output of the divider 40 to generate a quadrature sinusoidal signal from the square wave output of the divider 40. Alternatively, the clock generator 41 can be located in the receiver. The divider 40 may be programmed by through the program input. This feature allows changes in the IF frequency to avoid interference from an external source.

[0046] The output of the divider 40 is coupled to the RF clock generator 47 where it is further divided by a number n by a second divider 42. The output of the second divider 42 provides a reference frequency to a phase lock loop (PLL) 43. The PLL includes a phase detector 45, a divide by M circuit 46 and a voltage controlled oscillator (VCO) 48. The output of the VCO 48 is fed back through the divide by M circuit 46 to the phase detector 45 where it is compared with the reference frequency. The phase detector 45 generates an error signal representative of the phase difference between the reference frequency and the output of the divide by M circuit 46. The error signal is fed back to the control input of the VCO 48 to adjust its output frequency f_VCOuntil the VCO 48 locks to a frequency which is a multiple of the reference frequency. The VCO 48 may be programmed by setting M via the controller through the program input to the divide by M circuit 46. The programmability resolution of the VCO frequency f_VCOis set by the reference frequency which also may be programmed by the controller; through the program input of the divider 42.

[0047] In the described exemplary embodiment, the VCO frequency is sufficiently separated (in frequency) from the RF frequency generated by the transmitter 12 to prevent VCO pulling and injection lock of the VCO. Transmitter leakage can pull the VCO frequency toward the RF frequency and actually cause the VCO to lock to the RF signal if their frequencies are close to each other. The problem is exasperated if the gain and tuning range of the VCO is large. If the frequency of the RF clocks is f_LO, then the VCO frequency can be defined as: f_VCO=Nf_LO/(N+1). This methodology is implemented with a divide by N circuit 50 coupled to the output of the VCO 48 in the PLL 43. The output of the VCO 48 and the output of the divide by N circuit 50 are coupled to a complex mixer 52 where they are multiplied together to generate the RF clocks. A filter 53 can be positioned at the output of the complex mixer to remove the harmonics and any residual mixing images of the RF clocks. The divide by N circuit can be programmable via the controller through the select input. For example, if N=2, then f_VCO=(⅔)f_LO, and if N=3, then f_VCO=(¾) f_LO.

[0048] A VCO frequency set at ⅔ the frequency of the RF clocks works well in the described exemplary embodiment because the transmitter output is sufficiently separated (in frequency) from the VCO frequency. In addition, the frequency of the RF clocks is high enough so that its harmonics and any residual mixing images such as f_VCO×1−(1/N)), 3f_VCO×1+(1/N), and 3f_VCO×1−(1/N)) are sufficiently separated (in frequency) from the transmitter output to relax the filtering requirements of the RF clocks. The filtering requirements do not have to be sharp because the filter can better distinguish between the harmonics and the residual images when they are separated in frequency. Programming the divide by N circuit 50 also provides for the quadrature outputs of the divide by N circuit. Otherwise, with an odd number programmed, the outputs of the divide by N circuit 50 would not be quadrature. For an odd number, the divider 50 outputs will be differential, but will not be 90 degrees out of phase, i.e., will not be I-Q signals.

[0049] In the described exemplary embodiment, the RF clocks are generated in the in the LO generator 14. This can be accomplished in various fashions including, by way of example, either generating the RF clocks in the VCO or using a polyphase circuit to generate the RF clocks. Regardless of the manner in which the RF clocks are generated, the mixer 52 will produce a spectrum of frequencies including the sum and difference frequencies, specifically, f_VCO×(1+(1/N)) and its image f_VCO×(1−(1/N)). To reject the image, the mixer 52 can be configured as a double quadrature mixer as depicted in FIG. 3. The double quadrature mixer includes one pair of mixers 55, 57 to generate the Q-clock and a second pair of mixers 59, 61 to generate the I-clock. The Q-clock mixers utilizes a first mixer 55 to mix the I output of the VCO 48 (see FIG. 2) with the Q output of the divider 40 and a second mixer 57 to mix the Q output of the VCO with the I output of the divider. The outputs of the first and second mixers are connected together to generate the Q-clock. Similarly, the I-clock mixers utilizes a first mixer 59 to mix the I output of the divider with the Q output of the VCO and a second mixer 61 to mix the Q output of the divider with the I output of the VCO. The outputs of the first and second mixers are connected together to generate the I-clock. This technique provides, very accurate I-Q clocks by combination of quadrature VCO and filtering. Because of the quadrature mixing, the accuracy of the I-Q clocks is not affected by the VCO inaccuracy, provided that the divide by N circuit generates quadrature outputs. This happens for even divide ratios, such as N=2.

[0050] Optimized performance is achieved through frequency planning and implemented by programmable dividers in the LO generator to select different ratios. Based on FIG. 2, all the dependencies of the frequencies are shown by the following equation:

[0051] f_LO=f_RF−(M×f_OSC/nL)(1+1/N)=f_OSC/L

[0052] where f_RFis frequency of the transmitter output.

[0053] Turning back to FIG. 2, the transmitter 12 includes a complex buffer 54 for coupling incoming I-Q modulated baseband signals to a programmable low-pass filter 56. The low-pass filter 56 can be programmed by the controller through the select input. The output of the low-pass filter 56 is coupled to complex mixers 58. The complex mixers 58 mixes the I-Q modulated baseband signals with the RF clocks from the LO generator to directly upconvert the baseband signals to the transmitting frequency. The upconverted signal is then coupled to an amplifier 60 and eventually a power amplifier (PA) 62 for transmission into free space through the antenna. A bandpass filter (not shown) may be disposed after the PA 62 to filter out unwanted frequencies before transmission through the antenna.

[0054] In the described exemplary embodiment, the transmitter can be configured to minimize spurious transmissions. Spurious transmissions in a direct conversion transmitter are generated mainly because of the nonlinearity of the complex mixers and the DC offsets at the input to the complex mixers. Accordingly, the complex mixers can be designed to meet a specified IIP3 (Input Intercept Point for the 3^rdHarmonic) for the maximum allowable spurs over the frequency spectrum of the communications standard. The DC offsets at the input to the complex mixers can be controlled by the physical size of the transistors.

[0055] In addition, the transmitter can be designed to minimize spurious transmission outside the frequency spectrum of the communications standard set by the FCC. There are two sources for these spurs: the LO generator and the transmitter. These spurs can be are suppressed by multiple filtering stages in the LO generator and transmitter. Specifically, in the LO generator, due to the complex mixing of the VCO signal with the output of the divide by N circuit, all the spurs are at least f_VCO/N away from the RF clocks. By setting N to 2, by way of example, these unwanted spurs will be sufficiently separated (in frequency) from the transmitted signal and are easily removed by conventional filters in the LO generator and transmitter. Thus, the spurs will be mainly limited to the harmonics of the transmitted signal, which are also sufficiently separated (in frequency) from the transmitted signal, and therefore, can be rejected with conventional filtering techniques. For further reduction in spurs, a dielectric filter may be placed after the PA in the transmitter.

[0056] In embodiments of the present invention utilizing a low-IF or direct conversion architecture, techniques are implemented to deal with the potential disturbance of the local oscillator by the PA. Since the LO generator has a frequency which coincides with the RF signal at the transmitter output, the large modulated signal at the PA output may pull the VCO frequency. The potential for this disturbance can be reduced by setting the VCO frequency far from the PA output frequency. To this end, an exemplary embodiment of the LO generator produces RF clocks whose frequency is close to the PA output frequency, as required in a low-IF or direct-conversion architectures, with a VCO operating at a frequency far from that of the RF clocks. One way of doing so is to use two VCO 864, 866, with frequencies of f₁and f₂respectively, and mix 868 their output to generate a clock at a higher frequency of f₁+f₂as shown in FIG. 4. With this approach, the VCO frequency will be away from the PA output frequency with an offset equal to f₁(or f₂). A bandpass filter 876 after the mixer can be used to reject the undesired signal at f₁−f₂. The maximum offset can be achieved when f₁is close to f₂.

[0057] An alternative embodiment for generating RF clocks far away in frequency from the VCO is to generate f₂by dividing the VCO output by N as shown in FIG. 5. The output of the VCO 864 (at f₁) is coupled to a divider 872. The output of the divider 872 (at f₂) is mixed with the VCO at mixer 868 to produce an RF clock frequency equal to: f_LO=f₁′(1+1/N), where f₁is the VCO frequency. A bandpass filter 874 at the mixer output can be used to reject the lower sideband located at f₁−f₁/N.

[0058] In another embodiment of the present invention, a single sideband mixing scheme is used for the LO generator. FIG. 6 shows a single sideband mixing scheme. This approach generates I and Q signals at the VCO 864 output. The output of the VCO 864 is coupled to a quadrature frequency divider 876 should be able to deliver quadrature outputs. Quadrature outputs will be realized if the divide ratio (N) is equal to two to the power of an integer (N=2ⁿ). The I signal output of the divider 876 is mixed with the I signal output of the VCO 864 by a mixer 878. Similarly, the Q signal output of the divider 876 is mixed with the Q signal output of the VCO 864 by a mixer 880.

[0059] Although a single sideband structure uses two mixers, this should not double the mixer power consumption, since the gain of the single sideband mixer will be twice as much. By utilizing a Gilbert cell (i.e., a current commutating mixer) for each mixer 878, 880, the addition or subtraction required in a single sideband mixer can be done by connecting the two mixers 878, 880 outputs and sharing a common load (e.g., an LC circuit). The current from the mixers is added or subtracted, depending on the polarity of the inputs, and then converted to a voltage by an LC load (not shown) resonating at the desired frequency.

[0060] FIG. 7 shows an LO generator architecture in accordance with an embodiment of the present invention. This architecture is similar to the architecture shown in FIG. 6, except that the LO generator architecture in FIG. 7 generates I-Q data. In a low-IF system, a quadrature LO is desirable for image rejection. In the described embodiment, the I and Q outputs of the VCO can be applied to a pair of single sideband mixer to generate quadrature LO signals. A quadrature VCO 48 produces I and Q signals at its output. Buffers are included to provide isolation between the VCO output and the LO generator output. The buffer 884 buffers the I output of the VCO 48. The buffer 886 buffers the Q output of the VCO 48. The buffer 888 combines the I and Q outputs of the buffers 884, 886. The signal from the buffer 888 is coupled to a frequency divider 890 where it is divided by N and separated into I and Q signals. The I-Q outputs of the divider 890 are buffered by buffer 892 and buffer 894. The I output of the divider 890 is coupled to a buffer 892 and the Q signal output of the divider 890 is coupled to a buffer 894. A first mixer 896 mixes the I signal output of the buffer 892 with the I signal output of the buffer 884. A second mixer 897 mixes the Q signal output from the buffer 894 with Q signal output from the buffer 886. A third mixer 898 mixes the Q signal output of the buffer 894 with the I signal output of the buffer 884. A fourth mixer 899 mixes the I signal output from the buffer 892 with the Q signal output from the buffer 886. The outputs of the first and second mixers 896, 897 are combined and coupled to buffer 900. The outputs of the third and fourth mixers 898, 899 are combined and coupled to buffer 902. LC circuits (not shown) can be positioned at the output of each buffer 900, 902 to provide a second-order filter which rejects the spurs and harmonics produced due to the mixing action in the LO generator.

[0061] Embodiments of the present invention which are integrated into a single IC may employ buffers configured as differential pairs with a current source to set the bias. With this configuration, if the amplitude of the buffer input is large enough, the signal amplitude at the output will be rather independent of the process parameters. This reduces the sensitivity of the design to temperature or process variation.

[0062] The lower sideband signal is ideally rejected with the described embodiment of the LO generator because of the quadrature mixing. However, in practice, because of the phase and amplitude inaccuracy at the VCO and divider outputs, a finite rejection is obtained. In single IC fully integrated embodiments of the present invention, the rejection is mainly limited to the matching between the devices on chip, and is typically about 30-40 dB. Since the lower sideband signal is 2×f₁/N away in frequency from the desired signal, by proper choice of N, it can be further attenuated with on-chip filtering.

[0063] Because of the hard switching action of the buffers, the mixers will effectively be switched by a square-wave signal. Thus, the divider output will be upconverted by the main harmonic of VCO (f₁), as well as its odd harmonics (n×f₁), with a conversion gain of 1/n. In addition, at the input of the mixer, because of the nonlinearity of the mixers, and the buffers preceding the mixers, all the odd harmonics of the input signals to the mixers will exist. Even harmonics, both at the LO and the input of the mixers can be neglected if a fully balanced configuration is used. Therefore, all the harmonics of VCO (n×f₁) will mix with all the harmonics of input (m×f₂), where f₂is equal to f₁/N. Because of the quadrature mixing, at each upconversion only one sideband appears at the mixer output. Upper or lower sideband rejection depends on the phase of the input and LO at each harmonic. For instance, for the main harmonics mixed with each other, the lower sideband is rejected, whereas when the main harmonic of the VCO mixes with the third harmonic of the divider output signal, the upper sideband is rejected. Table 1 gives a summary of the cross-modulation products up to the 5^thharmonic of the VCO and input. In each product, only one sideband is considered, since the other one is attenuated due to quadrature mixing, and is negligible.

[0064] All the spurs are at least 2×f₁/N away from the main signal located at f₁×(1+1/N). The VCO frequency will be f₁/N away from the PA output. Thus, by choosing a smaller N better filtering can be obtained. In addition, the VCO frequency will be further away from the PA output frequency. The value of N, and the quality factor (Q) of the resonators (not shown) positioned at the output of each component determine how much each spur will be attenuated. The resonator quality factor is usually set by the inductor Q, and that depends merely on the IC technology. Higher Q provides better filtering and lower power consumption.

[0065] The maximum filtering is obtained by choosing N=1. Moreover, in this case, the frequency divider is eliminated. This lowers the power consumption and reduces the system complexity of the LO generator. However, the choice of N=1 may not be practical for certain embodiments of the present invention employing a low-IF receiver architecture with quadrature LO signals. The problem arises from the fact that the third harmonic of the VCO (at 3f₁) mixed with the divider output (at f₁) also produces a signal at 2f₁which has the same frequency as the main component of the RF clock output from the LO generator. With the configuration shown in FIG. 7, the following relations hold for the main harmonics:

[0066] Cos(ω₁t)·Cos(ω₁t)−Sin(ω₁t)·Sin(ω₁t)→Cos(2ω₁t)  (45)

[0067] and

[0068] Cos(ω₁t)·Sin(ω₁t)+Sin(ω₁t)·Cos(ω₁t)→Sin(2ω₁t)  (46)

[0069] which show that at the output of the mixers, quadrature signals at twice the VCO frequency exist. For the VCO third harmonic mixed with the divider output, however, the following relations hold:

[0070] −Cos(ω₁t)·⅓ Cos(3ω₁t)−Sin(ω₁t)·⅓ Sin(3ω₁t)→−⅓ Cos(2ω₁t)  (47)

[0071] and

[0072] Cos(ω₁t)·⅓ Sin(3ω₁t)−Sin(ω₁t) ⅓ Cos(3ω₁t)→−⅓ Sin(2ω₁t)  (48)

[0073] The factor ⅓ appears in the above equations because the third harmonic of a square-wave has an amplitude which is one third of the main harmonic. Comparing equation (46) with equation (48), the two products are added in equation (46), while they are subtracted in equation (47). The reason is that for the main harmonic of the VCO, quadrature outputs have phases of 0 and 90°, whereas for the third harmonic, the phases are 0 and 270°. The same holds true for equation (45) and equation (47). The two cosines in equation (45) and equation (47), when added, give a cosine at 2ω₁with an amplitude of 2/3, yet the two sinewaves in equation (46) and equation (48) when added, give a component at 2ω₁with an amplitude of 4/3. Therefore, a significant amplitude imbalance exists at the I and Q outputs of the mixers. When these signals pass through the nonlinear buffer at the mixers output, the amplitude imbalance will be reduced. However, because of the AM to PM conversion, some phase inaccuracy will be introduced. The accuracy can be improved with a quadrature generator, such as a polyphase filter, after the mixers. A polyphase filter, however, is lossy, especially at high frequency, and it can load its previous stage considerably. This increases the LO generator power consumption significantly, and renders the choice of N=1 unattractive for embodiments of the present invention employing a low-IF receiver architecture with quadrature LO signals.

[0074] For N=2, the LO generator output will have a frequency of 1.5f₁, and the closest spurs will be located ±f₁away from the output. These spurs can be rejected by positioning LC filters (not shown) at the output of each circuit in the LO generator. A second-order LC filter tuned to f₀, with a quality factor Q, rejects a signal at a frequency of f as given in the following equation: $\begin{array}{cc}\left|H\left(f\right)\right|=\frac{\frac{f}{{\mathrm{Qf}}_0}}{\sqrt{{\left[1-{\left(\frac{f}{f_0}\right)}^2\right]}^2+{\left(\frac{f}{{\mathrm{Qf}}_0}\right)}^2}}& \left(49\right)\end{array}$

[0075] The following discussion changes based on the Q value. Considering a Q of about 5 for the inductor, with f₀=1.5f₁, the spur located at 2.5f₁is rejected by about 15 dB by each LC circuit. This spur is produced at the LO generator output due to the mixing of the VCO third harmonic (at 3f₁) with the divider output (at 0.5f₁). This signal is attenuated by 10 dB since the third harmonic of a square-wave is one third of the main harmonic, 15 dB at the LC resonator at the mixers output tuned to 1.5f₁, and another 15 dB at the output of the buffers (900, 902 in FIG. 7). This gives a total rejection of 40 dB. When applied to the mixers in the transmitter, this LO generator output will upconvert the baseband data to 2.5f₁. With LC filters (not shown) positioned at the upconversion mixers and PA output in the transmitter, another 15+15=30 dB rejection is obtained (FIG. 7).

[0076] The spur located at 0.5f₁is produced because of the third harmonic of the divider output (at 1.5f₁) is mixed with the VCO output (at f₁). Because of the hard switching action at the divider output, the third harmonic is about 10 dB lower than the main harmonic at 0.5f₁. The buffer at the divider output tuned to 0.5f₁(892, 8943 in FIG. 7), rejects this signal by about 22 dB (equation (24)). This spur can be further attenuated by LC circuits:. at the mixer and its buffer output by (2)(22)=44 dB. The total rejection is 76 dB.

[0077] FIG. 8 shows a signal passing through a limiting buffer 910 (such as the buffers implemented in the LO generator). When a large signal at a frequency of f accompanied with a small interferer at a frequency of Δf 902 away pass through a limiting buffer, at the limiter output the interferer produces two tones ±Δf 914, 916 away from the main signal, each with 6 dB lower amplitude. Therefore, the spur at 2.5f₁will actually be 10+15+15+6=46 dB attenuated when it passes through the buffer, instead of the 40 dB calculated above. It will also produce an image at 0.5f₁which is 10+15+22+6=53 dB lower than the main signal. This will dominate the spur at 0.5f₁because of the third harmonic of the divider mixed with the VCO signal, which is more than 75 dB lower than the main signal.

[0078] Since the buffer is nonlinear, another major spur at the LO generator output is the third harmonic of the main signal located at 3×1.5f₁. This signal will be 10+22=32 dB lower than the main harmonic. The 22 dB rejection results from an LC circuit (not shown) tuned to 1155f₁(equation (49)) in the buffer. This undesired signal will not degrade the LO generator performance, since even if a perfect sinewave is applied to upconversion (or downconversion) mixers, due to hard switching action of the buffer, the mixer is actually switched by a square-wave whose third harmonic is only 10 dB lower. Thus, if a nonlinear PA is used in the transmitter, even with a perfect input to the PA, the third harmonic at the transmitter output will be 10+22+10=42 dB lower. The first 10 dB is because the third harmonic of a square-wave is one third of the main one, the 22 dB is due to the LC filter at the PA output, and the last 10 dB is because the data is spread in the frequency domain by three times. Any DC offset at the mixer input in the transmitter is upconverted by the LO, and produces a spur at f₁. This spur can be attenuated by 13 dB for each LC circuit used (equation (49)). In addition, the signal at the mixer input in the transmitter is considerably larger (about 10-20 times) than the DC offset. Thus the spur at f₁will be about 13+13+26=52 dB lower than the main signal. All other spurs given in Table 1 are more than 55 dB lower at the LO generator output. The dominant spur is the one at 2.5f₁which is about 46 dB lower than the main signal.

[0079] Choosing N>2 may not provide much benefit for single IC embodiments of the present invention with the possible exception that the on-chip filtering requirements may be relaxed. When using an odd number for N, further disadvantages may be realized because the divider output will not be in quadrature thereby preventing single sideband mixing. In addition, for N>2 the divider becomes more complex and the power consumption increases. Nevertheless, in certain applications, N=4 may be selected over N=2 so that the divider quadrature accuracy will not depend on the duty cycle of the input signal.

[0080] When choosing N equal to 2ⁿ, such as N=2, quadrature signals are readily available at the divider output despite quadrature phase inaccuracies at the output of the VCO. Assume that the VCO outputs have phase of 0 and 90°+q, where q is ideally 0, and that the divider produces perfect quadrature outputs. At the LO generator outputs the following signals exist:

[0081] V_out1=Cos(ω₂t)·Cos(ω₁t+θ)−Sin(ω₂t)·Sin(ω₁t)  (50)

[0082] and

[0083] V_outQ=Cos(ω₂t)·Sin(ω₁t)+Sin(ω₂t)·Cos(ω₁t+θ)  (51)

[0084] where ω₁is the VCO radian frequency, and ω₂is the divider radian frequency, equal to 0.5ω₁. By simplifying equation (25) and equation (26), the signals at the output of mixers will be: $\begin{array}{cc}{V}_{{\mathrm{out}}_{—}I}=-\mathrm{Sin}\left(\frac{\theta }{2}\right)·\mathrm{Sin}\left(\left({\omega }_1-{\omega }_2\right)t+\frac{\theta }{2}\right)+\mathrm{Cos}\left(\frac{\theta }{2}\right)·\mathrm{Cos}\left(\left({\omega }_1+{\omega }_2\right)t+\frac{\theta }{2}\right)\mathrm{and}& \left(52\right)\\ V_{{\mathrm{out}}_{—}Q}=-\mathrm{Sin}\left(\frac{\theta }{2}\right)·\mathrm{Cos}\left(\left({\omega }_1-{\omega }_2\right)t+\frac{\theta }{2}\right)+\mathrm{Cos}\left(\frac{\theta }{2}\right)·\mathrm{Sin}\left(\left({\omega }_1+{\omega }_2\right)t+\frac{\theta }{2}\right)& \left(53\right)\end{array}$

[0085] The above equations show that regardless of the value of θ, the outputs are always in quadrature. However, other effects should be evaluated. First, a spur at ω₁−ω₂=0.5ω₁is produced at the output. This spur can be attenuated by 2×22=44 dB by the LC filters at the mixer and its buffer outputs. Thus, for 60 dB rejection, the single sideband mixers need to provide an additional 16 dB of rejection (about 0.158). Based on equation (53), tan(θ/2)=0.158, or θ≈18°, phase accuracy of better than 18° can generally be achieved. Second, phase error at the VCO output lowers the mixer gain (term Cos(θ/2) in equation (52) or (53)). For a phase error of 18°, the gain reduction is, however, only 0.1 dB, which is negligible. For θ=90° (a single-phase VCO), both sidebands are equally upconverted at the mixer output. However, the LC filters reject the lower sideband by about 44 dB. The mixer gain will also be 3 dB lower. This will slightly increase the power consumption of the LO generator. If θ=180° (the VCO I and Q outputs are switched), the lower sideband is selected, and the desired sideband is completely rejected.

[0086] Similarly, the LO generator will not be sensitive to the phase imbalance of the divider outputs if the VCO is ideal. However, if there is some phase inaccuracy at both the divider and VCO outputs, the LO generator outputs will no longer be in quadrature. In fact, if the VCO output has a phase error of q₁and the divider output has a phase error of q₂, the LO generator outputs will be: $\begin{array}{cc}{V}_{{\mathrm{out}}_{—}I}=-\mathrm{Sin}\left(\frac{{\theta }_1-{\theta }_2}{2}\right)·\mathrm{Sin}\left(\left({\omega }_1-{\omega }_2\right)t+\frac{{\theta }_1-{\theta }_2}{2}\right)+\mathrm{Cos}\left(\frac{{\theta }_1+{\theta }_2}{2}\right)·\mathrm{Cos}\left(\left({\omega }_1+{\omega }_2\right)t+\frac{{\theta }_1+{\theta }_2}{2}\right)\mathrm{and}& \left(54\right)\\ V_{{\mathrm{out}}_{—}Q}=-\mathrm{Sin}\left(\frac{{\theta }_1+{\theta }_2}{2}\right)·\mathrm{Cos}\left(\left({\omega }_1-{\omega }_2\right)t+\frac{{\theta }_1-{\theta }_2}{2}\right)+\mathrm{Cos}\left(\frac{{\theta }_1-{\theta }_2}{2}\right)·\mathrm{Sin}\left(\left({\omega }_1+{\omega }_2\right)t+\frac{{\theta }_1+{\theta }_2}{2}\right)& \left(55\right)\end{array}$

[0087] This shows that the outputs still have phases of 0 and 90°, but their amplitudes are not equal. The amplitude imbalance is equal to: $\begin{array}{cc}\frac{\Delta A}{A}=2\frac{\mathrm{Cos}\left(\frac{{\theta }_1+{\theta }_2}{2}\right)-\mathrm{Cos}\left(\frac{{\theta }_1-{\theta }_2}{2}\right)}{\mathrm{Cos}\left(\frac{{\theta }_1+{\theta }_2}{2}\right)+\mathrm{Cos}\left(\frac{{\theta }_1-{\theta }_2}{2}\right)}=2\tan \left(\frac{{\theta }_1}{2}\right)\times \tan \left(\frac{{\theta }_2}{2}\right)& \left(56\right)\end{array}$

[0088] If θ₁and θ₂are small and have an equal standard deviation, that is, the phase errors in the VCO and divider are the same in nature, then the output amplitude standard deviation will be: $\begin{array}{cc}{\sigma }_A\approx \frac{{\left({\sigma }_{\theta }\right)}^2}{2}& \left(57\right)\end{array}$

[0089] where σ_Ais the standard deviation of the output amplitude, and σ₀is the phase standard deviation in radians. Equation (57) denotes that the phase inaccuracy in the VCO and divider has a second order effect on the LO generator. For instance, if θ₁and θ₂are on the same order and about 10°, the amplitude imbalance of the output signals will be only about 1.5%. In this case, the lower sideband will be about 15 dB rejected by the mixers, which will lead to a total attenuation of about 22+22+15=59 dB. This shows that the LO generator is robust to phase errors at the VCO or divider outputs, since typically phase errors of less than 5° can be obtained on chip.

[0090] Phase errors in the divider can originate from the mismatch at its output. Moreover, for N=2, if the input of the divider does not have a 50% duty cycle, the outputs will not be in quadrature. Again, the deviation from a 50% duty cycle in the divider input signal may be caused due to mismatch. Typically, with a careful layout, this mismatch is minimized to a few percent. The latter problem can also be alleviated by improving the common-mode rejection of the buffer preceding the divider (888 in FIG. 7). One possible way of doing so is to add a small resistor at the common tail of the inductors in the buffer. For a differential output, this resistor does not load the resonator at the buffer output, since the inductors common tail is at AC ground. A common-mode signal at the output is suppressed however, since this resistor degrades the LC circuit quality factor. The value of the resistor should be chosen appropriately so as not to produce a headroom problem in the buffer.

[0091] Embodiments of the present invention that are fully integrated onto a single IC can be implemented with a wide tuning range VCO with constant gain. In a typical IC process, the capacitance can vary by 20%. This translates to a 10% variation in the center frequency of the oscillator. A wide tuning range can be used to compensate for variation. Variations in temperature and supply voltage can also shift the center frequency. To generate a wide tuning range, two identical oscillators can be coupled together as shown in FIG. 9. This approach forces the oscillation to be dependent on the amount of coupling between the two oscillators.

[0092] In the described exemplary embodiment of the VCO shown in FIG. 9, the tuning curve is divided into segments with each segment digitally selected. This approach ensures a sufficient amount of coupling between the two oscillators for injection lock. In addition, good phase noise performance is also obtained. The narrow frequency segment prevents the gain of the VCO from saturating. The segmentation lowers the VCO gain by the number of segments, and finally by scaling the individual segments, a piecewise linear version of the tuning curve is made resulting in a constant gain VCO.

[0093] FIG. 9 shows a block diagram of the wide tuning range VCO comprising two coupled oscillators where the amount of coupling transconductance is variable. The wide tuning range VCO comprises two resonators 800, 802 and four transconductance cells, g_mcells 804, 806, 808, 810. The transconductance cells are driver that converts voltage to current. The transconductance cells used to couple the oscillators together have a variable gain. The first VCO 800 provides the I signal and the second VCO provides the Q signal. The output of the first VCO 800 and the output of the second VCO 802 are coupled to transconductance cells 806, 807, respectively, combined, and fed back to the first VCO 800. The transconductance cell 807 used for feeding back the output of the second VCO to the first VCO is a programable variable gain cell. Similarly, the output of the second VCO 802 and the output of the first VCO 800 are coupled to transconductance cells 805, 804, respectively, combined, and fed back to the second VCO 802. The transconductance cell 804 used for feeding back the output of the first VCO to the second VCO is a programmable variable gain cell. The gain of the programmable variable gain transconductance cells 804, 807 can be digitally controlled from the controller

[0094] FIG. 10 shows a schematic block diagram of the wide-tuning range VCO described in connection with FIG. 9. The wide-tuning range VCO includes individual current sources 810, 812, 814, 816, cross-coupled transistors 818, 820 with resonating inductors 826, 828, and cross-coupled transistors 822, 824 with resonating inductors 830, 832. Two differential pairs couple the two sets of oscillators. Differential pair 834, 836 are coupled to the drains of transistors 824, 822, respectively. Differential pair 838, 840 are coupled to the drains of transistors 818, 820. Tank #1 comprises inductors 826 and 828. Tank #2 comprises inductors 830 and 832.

[0095] Transistors 818 and 820 form a cross-coupled pair that injects a current into tank #1 in which the current through the transistor 818 is exactly 180 degrees out of phase with the current in the transistor 820. Likewise, transistors 822 and 824 form a cross-coupled pair that injects a current into tank #2 in which the current through the transistor 822 is exactly 180 degrees out of phase with the current in the transistor 824. The first set of coupling devices 834, 836 injects a current into tank #1 that is 90 degrees out of phase with current injected respectively by the transistors 818, 820. The second set of coupling devices 838, 840 injects a current into tank #2 that is 90 degrees out of phase with the current injected respectively by the transistors 822, 824. The tank impedances causes a frequency dependent phase shift. By varying the amplitude of the coupled signals, the frequency of oscillation changes until the phase shift through the tanks results in a steady-state solution. Varying the bias of the current source controls the gm of the coupling devices. Current sources 812, 816 provide control of VCO tuning. Current sources 810, 814 provide segmentation of the VCO tuning range.

[0096] FIG. 11 shows the typical tuning curve of the wide tuning range VCO before and after segmentation. The horizontal axis is voltage. The vertical axis is frequency. FIG. 12 shows how segmentation is used to divide the tuning range and linearize the tuning curve. The linear tuning curves correspond to different VCO segments. The slope of the linear tuning curves is a result control of VCO tuning. The horizontal axis is voltage. The vertical axis is frequency.

[0097] FIG. 13 shows how the VCO of FIG. 9 can be connected to the divider before being upconverted to the RF clock frequency in the LO generator. The I output signal of the VCO is coupled to buffer 884 and the Q output signal of the VCO is coupled to buffer 886. Buffer 888 combines the I-Q data from the buffer 884 and the buffer 886 to obtain a larger signal. The large signal is coupled to a divider 50 where it is divided in frequency by N to get quadrature signals.

[0098] In another embodiment of the present invention, a polyphase filter 892 follows a single-phase VCO as shown in FIG. 14. This approach uses a single phase VCO 48 with a polyphase filter 892 to get quadrature signals. The output of the VCO 48 is coupled to a buffer 888. The buffer provides sufficient drive for the polyphase filter 892.

[0099] A multiple stage polyphase filter can be used to obtain better phase accuracy at a certain frequency range. Embodiments of the present invention that are fully integrated into a single IC, the required frequency range is mainly set by the process variation on the chip and the system bandwidth.

[0100] Any amplitude imbalance in the signals at the VCO and divider output will only cause a second order mismatch in the amplitude of the LO generator signals, and the output phase will remain 0 and 90°. If the standard deviation of the amplitude imbalance at the VCO and divider are the same and equal to σ_a, then the standard deviation of the LO generator output amplitude imbalance (σ_A) will be: $\begin{array}{cc}{\sigma }_A=\frac{{\left({\sigma }_{\alpha }\right)}^2}{2}& \left(58\right)\end{array}$

[0101] The reason phase inaccuracy is more emphasized here is that because of the limiting stages in the LO generator and the hard switching at the mixers LO input, most of the errors will be in phase, rather than amplitude.

[0102] Although the phase or amplitude inaccuracy at the mixers input or LO has only a second order effect on the LO generator, any mismatch at the mixers outputs or the following stages will directly cause phase and amplitude imbalance in the LO generator outputs. This mismatch will typically be a few percent, and will not adversely impact the transceiver performance, since in a low-IF or direct conversion architectures the required image rejection is usually relaxed.

[0103] Although a preferred embodiment of the present invention has been described, it should not be construed to limit the scope of the appended claims. For example, the present invention can be into a single integrated circuit, can be constructed from discrete components, or can include one or more integrated circuits supported by discrete components. Those skilled in the art will understand that various modifications may be made to the described embodiments. Moreover, to those skilled in the various arts, the invention itself herein will suggest solutions to other tasks and adaptations for other applications. It is therefore desired that the present embodiments be considered in all respects as illustrative and not restrictive, reference being made to the appended claims rather than the foregoing description to indicate the scope of the invention.