Sigma-delta modulator and method for suppressing a quantization error in a sigma-delta modulator

[0002] 1. Field of the Invention

[0003] The present invention relates to a sigma-delta modulator for conversion of a an analog or digital low-frequency input signal of a high resolution into a quantized analog or digital signal, which has an error feedback circuit for suppression of quantization errors. It also relates to a method for suppressing quantization errors in this type of sigma-delta modulator.

[0004] 2. Prior Art

[0005] Sigma-delta modulators convert low frequency signals of high resolution, which can be in analog or digital form, into scanned, coarse quantized signals with a comparatively high scan rate. This output signal can similarly be prepared in analog or digital form. Quantization noise arises because of this coarse quantization (often only a single bit is used for the quantization). An attempt is made to shape this noise by error feedback so that the noise spectrum in the interesting low frequency band (the frequency band for the input signal) is very small, but increases at higher frequencies. High frequency noise may be largely eliminated by a low-pass filter.

[0006] A sigma-delta modulator can be used, for example, as an analog/digital converter (A/D converter); an analog input signal is converted into a high frequency digital pulse sequence with a weight of ±1, for example. The reverse, namely the use of a sigma-delta modulator as a digital/analog converter (D/A converter), is also possible. The digital input signal, for example, has a 16-bit word length with a scanning rate of, e.g., 48 kHz. The output signal can be, for example, a high frequency sequence of discrete analog values (for example ±1 volt with a scanning rate of 1 MHz). A sigma-delta modulator can also be used as a digital/digital converter (D/D converter), which converts a digital pulse sequence of high resolution (e.g. 16 it) and low scanning rate (e.g. 48 kHz) into a digital pulse sequence of low resolution (e.g. 1 bit) and high scanning rate (e.g. 1 Mz). An application for this type of D/D converter is described, e.g., in DE-A 198 19 069. This publication shows that an analog signal can be multiplied with a digital signal with the help of a purely digital sigma-delta modulator. This principle is used there for analysis of an analog sensor signal. Sigma-delta modulators of 2^ndorder with a one bit quantization are, for example, described in the article “A Use of Double Integration in Sigma Delta Modulation”, by J. Candy, IEEE, Transactions on Communications”, March 1985. The modulator described there comprises a 1^storder modulator, which has an added feedback loop. It was pointed out in this reference that in the case of 1 bit quantization further feedback loops for increasing the modulation degree (degree ≧3) lead to unstable structures.

[0007] Topologies that guarantee the stability of a sigma-delta modulator with 1 bit quantization with suitable dimensions are described in “Theory and Practical Implementation of a Fifth-Order Sigma-Delta AID Converter”, by R. W. Adams, et al, J. Audio Eng. Soc., Vol. 39, Nr. 718, 1991. The named article relates, for example, to an A/D converter with a 5^thorder sigma-delta modulator and a 1-bit quantization.

[0008] Sigma-delta modulators can also be used for other purposes than for A/D or D/A converter. For example, the use of several purely digital sigma-delta modulators inside an IIR filter was described in “IIR Filtering on Sigma-delta Modulated Signals”, D. A. Johns, et al, Electronics Letters 14, February 1991, Vol. 27, Nr. 4. Non-linear operations on a data stream of a sigma-delta modulator is described in “Nonlinear Arithmetic Operations on the Delta Sigma Pulse Stream”, M. Freeman, et al, Signal Processing 21, Elsevier Science Publishers, pp. 25 to 35 (1990).

[0009] It is an object of the present invention to provide a sigma-delta modulator in which quantization errors or quantization noise can be suppressed in an effective manner.

[0010] This object is attained by a sigma-delta modulator for conversion of an analog or digital low frequency input signal of high resolution into a quantized analog or digital signal, with an error feedback circuit for suppression of quantization errors, which comprises

[0011] means for delaying the input signal X for a plurality of time intervals to obtain a plurality of delayed input signals X_iwherein i=1, 2, . . . , n and the ith one of the delayed input signals Xi is delayed for i scanning periods;

[0012] means for addition of the delayed input signals X_ieach delayed by i scanning periods to obtain a sum signal S_i;

[0013] means for producing quantized input signals VZ_ieach delayed by the i scanning periods;

[0014] means for addition of the delayed quantized input signals VZ_ito obtain a second sum signal S₂; and

[0015] means for subtraction of the sum signals S₁and S₂from the actual value of the input signal.

[0016] The value of n corresponding to a desired order of the sigma-delta modulator can be, e.g., between 1 and 20. Also other values are conceivable, for example n=5. Good results may be obtained, e.g., also with a 3^rdorder sigmadelta modulator (n=3). A very effective suppression of quantization noise takes place in the sigma-delta modulator according to the invention.

[0017] The object of the invention is also attained by a method of suppressing quantization errors occurring in the conversion of an analog or digital low frequency input signal X of high resolution to a quantized analog or digital signal Y in a sigma-delta modulator having an error feedback circuit. This method has the following steps:

[0018] a) quantizing the input signal X according to a scanning rate f_Aat a time t=m·Ta , wherein m=0,1,2, . . . and Ta is the scanning period of the sigma-delta modulator;

[0019] b) delaying the input signal for plurality of time intervals to obtain a plurality of delayed input signals X_iwherein i=1, 2, . . . , n and the ith delayed input signal is delayed for i scanning periods;

[0020] c) adding the delayed input signals X_ieach delayed for i scanning periods to obtain a first sum signal S_i;

[0021] d) producing quantized input signals and delaying them by a plurality of time intervals to obtain a plurality of delayed quantized input signals VZ_iwherein i=1, 2, . . . , n and the ith quantized input signal is delayed for i scanning periods;

[0022] e) adding the delayed quantized input signals VZ_ito obtain a second sum signal S₂; and

[0023] f) subtracting the sum signals S₁and S₂from the actual value of the input signal X.

[0024] Advantageous embodiments of the sigma-delta modulator and the method according to the invention are set forth the appended dependent claims and additional description below.

[0025] According to a preferred embodiment of the sigma-delta modulator it has means for multiplying the respective delayed input signals X_iwith respective coefficients d_iof a transformation function so that the first sum S₁can be represented by S₁=Σd_iX_iand means for multiplying the respective delayed, quantized input signals VZ_iwith respective coefficients c_iof the transformation function so that the second sum S₂can be represented by S₂=Σc_iVZ_i. The transformation function of the sigma-delta modulator according to the invention is, for example, representable in the following form:

[0026] Y(z)=X(z)·{a₀/[1+(c₁+d₁)·z⁻¹+(c₂+d₂)·z⁻²+ . . . +(c_n+d_n)·z⁻ⁿ]}

[0027] +E(z)·{[1+d₁·z⁻¹+d₂·z⁻²+ . . . +d_n·z⁻ⁿ]/[1+(c₁+d₁)·z⁻¹+(c₂+d₂)·z⁻²+ . . . +(c_n+d_n)·z⁻ⁿ]}  (1)

[0028] The transformation function of the system is represented here with the help of a Z transformation. Z is a frequency variable for representation of the transformation function in frequency space. X(z) or Y(z) is the Z-transformed (frequency spectrum) input signal X or the output signal Y. E(z) represents the Z-transformed (frequency spectrum) noise signal. The occurring quantization error e is defined as the difference between the input and output signal of a suitable quantization. The numerator and the denominator of the noise transformation function (factor for E(z)) and the denominator of the signal transformation function (factor for X(z)) may be adjusted by choice of the coefficients c_iand d_iperformed according to the invention. Usually the signal transformation function is dimensioned as a low-pass filter and the noise transformation is dimensioned as a high-pass filter, whereby the resulting noise in the output signal Y can be kept small in the low frequency band (i.e. in the frequency band of the input signal).

[0029] Advantageously the sigma-delta modulator according to the present invention has means for depositing or storing 2ⁿpossible states of the second sum signal S₂according to the transformation function and the corresponding choice for the coefficients c_i, so that a particular or specific state is detectable without the necessity of explicitly performing the summation operation and is output as a suitable sum signal S₂. Since the quantized signals VZ₁, VZ₂, . . . , VZ_n(respectively ±1) can take only 2ⁿdifferent states the fact that the sum ΣVZ_ic_ineed not be computed in each scanning step is guaranteed. Furthermore all possible 2ⁿdifferent results can be computed in advance and stored in a suitable manner. The computational work is therefore substantially reduced in comparison to conventional sigma-delta modulators because of the reduction of the multiplication and addition operations.

[0030] The objects, features and advantages of the invention will now be illustrated in more detail with the aid of the following description of the preferred embodiments, with reference to the accompanying figures in which:

[0031] FIG. 1 is a schematic block diagram of an nth order sigma-delta modulator according to the invention;

[0032] FIG. 2 is a schematic block diagram of the structure of a sigma-delta modulator with a separate delay chain for the quantized signal according to the invention;

[0033] FIG. 3 is a schematic block diagram of an A/D converter comprising a sigma-delta modulator according to the invention;

[0034] FIG. 4 is a schematic block diagram of a D/D converter comprising a sigma-delta modulator according to the invention; and

[0035] FIG. 5 is a schematic block diagram of a D/A converter comprising a sigma-delta modulator according to the invention.

[0036] In FIG. 1 the basic structure of an nth order sigma-delta modulator according to the invention is shown. X represents the analog or digital input signal and Y represents the analog or digital quantized output signal at discrete time points m·Ta (m=0, 1, 2, . . . ). The Ta represents the scanning period of the sigma-delta modulator.

[0037] The triangular blocks represent means d₁,d₂,d₃; c₁,c₂,c₃for multiplying an input signal with the respective entered coefficients c_ior d_i(multiplication component). The drawing figure is simplified by using the respective coefficient multiplier as the reference symbol for the respective means for multiplying. The circles 1, 2 and 3 represent means for addition. The symbol Z⁻¹indicates a delay of about one scanning period Ta.

[0038] Means for quantizing are indicated with the reference characters Q₀, Q₁, Q_n, which perform a coarse quantization of an input signal. The quantization usually results in only two possible values, for example ±1 in the case of a digital quantization, or ±U_refin the case of an analog quantization and a reference voltage U_ref, which can amount to, e.g., 1 volt.

[0039] The transformation function of the system can be represented with the help of the Z transformation in the following form:

[0040] Y(z)=X(z)·{a₀/[1+(c₁+d₁)·z⁻¹+(c₂+d₂)·z⁻²+ . . . +(c_n+d_n)·z⁻ⁿ]}

[0041] +E(z)·{[1+d₁·z⁻¹+d₂·z⁻²+ . . . +d_n·z⁻ⁿ]/[1+(c₁+d₁)·z⁻¹+(c₂+d₂)·z⁻²+ . . . +(c_n+d_n)·z⁻ⁿ]}  (1)

[0042] Here, as already mentioned above, X(z) or Y(z) are the Z-transformations of the respective input signal X or output signal Y. E(z) represents the Z-transformation of the quantization error e(m·Ta) originating from upmost quantizer Q₁. The occurring quantization error is defined as the difference between the input and output signal of a suitable quantization.

[0043] A suitable form for the transformation function (1) results by means of suitable selection of the coefficients c_ior d_i.

[0044] The input signal X is first multiplied with the coefficient a₀. Subsequently the resulting signal is input to a quantizer Q₀to obtain the output signal Y. The signal fed to the quantizer Q₀can be modified by means of an error feedback circuit. The error feedback circuit has delay elements Z⁻¹₁, Z⁻¹₂, Z⁻¹₃; quantizers Q₁to Q_n, and means d₁,d₂,d₃; c₁,c₂,c₃for multiplying the transformed function Y(Z) with the coefficients c_ito c_nor d_ito d_n. After a delay by a first delay element Z⁻¹₁an input signal quantity X is fed to a means d₁for multiplying, a further delay element Z¹₂and a second quantizer Q₁as delayed input signal quantity X₁. The second delay element Z⁻¹₂correspondingly feeds a delayed input signal quantity X₂delayed by about two scanning periods to a second means d₂for multiplying, a further delay element Z⁻¹and a further quantizer Q₂. A suitable delay and further conduction of the delayed input signal to an nth delay element Z⁻¹occurs according to the order of the sigma-delta modulator.

[0045] The delayed input signals X_imultiplied by the coefficients d₁to d_nare input to the means 2 for addition, in which a first sum Σd_iX_iis formed.

[0046] The delayed input signals X_iare fed further to the quantizers Q₁to Q_n. A coarse quantization of the delayed input signals X_ioccurs in the quantizers Q₁to Q_n.

[0047] Usually the signs VZ₁to VZ_nappear at the respective outputs of the quantizers Q₁to Q_n. The output VZ₁to VZ_nare multiplied by the respective coefficents c₁to c_n. The resulting products are fed to a means 3 for adding to form a second sum Σc_iVZ_i.

[0048] The sums computed by the means 2,3 for adding are input to a means 1 for subtracting, and there subtracted from the actual value of the input signal X.

[0049] An additional embodiment of the sigma-delta modulator according to the invention is shown in FIG. 2. The embodiment of FIG. 2 provides an alternative to the embodiment of FIG. 1, in which only one quantizer Q is provided. A separate delay network is provided for the quantized signal. The transformed signal or the error feedback occurs in the analogous manner to the embodiment of FIG. 1.

[0050] In the embodiment of the sigma-delta modulator according to FIG. 3 the input signal X is an analog signal. Thus the adders 1,2, the multipliers a₀, d₁to d_nand the linked delay network or chain with the delay elements Z⁻¹are embodied in analog technology. Analog delay chains are usually embodied in SC technology (switched capacitor) according to the state of the art. The quantizer Q can, for example, by formed as a comparator, which supplies a digital signal at its output. With 1 bit quantization this digital signal is, for example, in the state ±1 (comparator input signal ≧0) and −1 (comparator input signal <0) and thus outputs the sign VZ of the input signal. The correct delay network with delay elements Z⁻¹is digital (for example 1 bit wide).

[0051] That the quantized signals VZ₁to VZ_n(respectively ±1) can only take 2ⁿdifferent states is a particular advantage of the sigma-delta modulator according to the invention. The embodiments shown with the fundamental structures shown in FIGS. 1 and 2 do not compute the sum Σc_iVZ_ito be formed according to the invention in each scanning step. It is sufficient to calculate in advance all possible 2ⁿdifferent results according to the chosen c_iand to store them. In that way multiplication and addition operations can be eliminated. In the case of the A/D converter shown in FIG. 3 this is accomplished by an analog multiplexer 10, which has n digital control inputs VZ₁to VZ_nand one of 2ⁿanalog voltages at its output. The analog voltages are derived from a reference potential ±U_ref(e.g. ±1 volt) by a passive voltage divider in a known manner. The required analog voltages are (±c₁, ±c₂, ±c_n)·U_refaccording to the selected coefficients c_iof the transformation function Y(z).

[0052] In FIG. 4 a D/D converter is shown, in which all the elements are digital. A plurality of quantizers Q₀to Q_nare provided according to the structure of the sigma-delta modulator of FIG. 4. These quantizers result in no additional circuit expense, since it is sufficient to quantize a signal of long word length (for example 16 bit) so that only the highest bit (sign it in the two's complement representation) is processed further. The preparation of the 2ⁿdigital values occurs here for example by means of a table, which can be provided as a ROM, or by a digital multiplexer 11, at whose inputs the above-described digital values VZ_iare applied.

[0053] In FIG. 5 a D/A converter is shown which is based on the sigma-delta modulator according to the invention. The structure correspond essentially to the structure of the D/D converter in FIG. 4, however an analog signal must be formed with both voltage values ±U_refat the output of the highest quantizer Q₀from the 1 bit signal. A table or a digital multiplexer 11 is provided again for storage of the 2ⁿpossible values of the second sum Σc_iVZ_i.

[0054] The disclosure in German Patent Application 198 51 637.1 of Nov. 10, 1998 is incorporated here by reference. This German Patent Application describes the invention described hereinabove and claimed in the claims appended hereinbelow and provides the basis for a claim of priority for the instant invention under 35 U.S.C. 119.

[0055] While the invention has been illustrated and described as embodied in a sigma-delta modulator and method for suppressing a quantization error in a sigma-delta modulator, it is not intended to be limited to the details shown, since various modifications and changes may be made without departing in any way from the spirit of the present invention.

[0056] Without further analysis, the foregoing will so fully reveal the gist of the present invention that others can, by applying current knowledge, readily adapt it for various applications without omitting features that, from the standpoint of prior art, fairly constitute essential characteristics of the generic or specific aspects of this invention.