Method and apparatus for testing delta-sigma modulators

Abstract: A delta-sigma modulator (14) is tested by sampling an input test signal at a first rate (in 24) and inputting the samples to the delta-sigma modulator under test so that the modulator outputs a digital signal representative of each sample. The input signal is also sampled at a second rate (in 26) and an error factor is then established (by 28) in accordance with the difference between the value of the output signal produced by the delta-sigma modulator and the value of the sample obtained by sampling the input signal at the second rate. By comparing the error factor to a prescribed value, the proper operation of the delta-sigma modulator can be verified.

Description: Technical Field This invention relates to a method and associated apparatus for testing delta-sigma modulators which are a particular class of devices for performing voltage-to-frequency conversion. Background of the Invention Delta-Sigma modulators are a class of voltage-to-frequency conversion devices. When coupled to a digital filter, the combination of the delta-sigma modulator and filter yields a delta-sigma modulator A/D converter with very high performance. A typical delta-sigma modulator functions as a voltage-to-frequency converter which produces an output voltage of + b or - b (where b is typically +1 volt) in accordance with the input voltage to the modulator. (When the input voltage is zero, the analog modulator output voltage is zero.) The digital signal produced by the delta-sigma modulator, when filtered by the digital filter, yields a serial signal representative of the level of the voltage input to the modulator. In the past, delta-sigma modulators have been tested by comparing whether the frequency domain value of the Signal-to-Noise (S/N) ratio of the modulator is significantly below a prescribed value. The frequency domain value of the S/N ratio has been established from a power spectrum density of the samples output by the delta-sigma modulator when samples of a sinusoidal signal is applied to its input. The power density spectrum has been computed by performing a Fourier transform on each output sample to obtain its value in the frequency domain, and thereafter multiplying the value by its conjugate. Testing the delta-sigma modulator in this fashion is a relatively complex undertaking. The complexity (i.e., number of operations) associated with performing a Fourier transform on n delta-sigma modulator output signals (where n is an integer) is n log( n ) complex multiplications. The complexity associated with establishing a power spectrum density of the n output signals by multiplying the Fourier transform of each signal by its complex conjugate is 2 n complex multiplications because the Fourier transform and complex conjugate of each signal are typically complex numbers. Lastly, the complexity associated with establishing the signal-to-noise ratio of the delta-sigma modulator from the power spectrum density of the samples output is approximately n real additions. Thus, the overall complexity associated with testing the delta-signal modulator in this manner is on the order of n log ( n ) + 2 n complex multiplications and n real additions. Thus, there is need for a technique for testing a delta-sigma modulator with reduced complexity. NACHRICHTEN TECHNIK ELEKTRONIK, Vol. 39, no. 12, 1989, pages 462-464, BERLIN, DD, LUDWIG, R., "Messung und Prüfung von Analog-Digital-Wandlern, Teil 2" discloses a technique for characterizing an analog-to-digital converter. An input signal, having a precise amplitude and frequency, is input to the converter. The converter is clocked at periodic intervals and the output signal is then compared to a reference signal representing the estimated output that the converter would produce for the known input signal. According to one aspect of this invention there is provided a method as claimed in claim 1. According to another aspect of this invention there is provided apparatus as claimed in claim 4. Briefly, a method is disclosed for testing a delta-sigma modulator with a reduced level of complexity. The method is initiated by sampling an input test signal at a first rate and inputting the samples to a delta-sigma modulator under test so that the modulator outputs a digital signal representative of each sample. The input signal is also sampled at a second rate, typically less than the first rate. An error factor is then established in accordance with the difference between the value of the output signal produced by the delta-sigma modulator and the value of the sample obtained by sampling the input signal at the second rate. By comparing the error factor to a prescribed value, the proper operation of the delta-sigma modulator can be verified. The above-described method may be practiced by choosing the second sampling rate (i.e., the rate at which the input signal is sampled for comparison purposes) to be the Nyquist rate. Choosing the second sampling rate to be equal to the Nyquist rate requires that the first sampling rate be made larger, so that the input test signal is "over-sampled". The error factor chosen to evaluate the delta-sigma modulator is its Signal-to-Noise (S/N) ratio. The actual S/N ratio of the delta-sigma modulator is established by first computing an intermediate error value ( e 2 ) in accordance with the sum of the square of the difference between each output signal of the modulator and each sample obtained by sampling the input signal at the Nyquist rate. The ratio of the delta-sigma modulator output signal magnitude ( b 2 ) to the intermediate error signal ( e 2 ) yields a measure of the actual S/N ratio of the delta-sigma modulator. By comparing the actual value of the S/N ratio of the delta-sigma modulator to the expected value therefor, the proper operation of the modulator can be determined. Alternatively, the testing method may be practiced by choosing the input signal to be a dc value and choosing the second sampling rate to be unity. The error value computed is the difference between the magnitude of the dc input signal to the delta-sigma modulator and the output signal of the delta-sigma modulator, as summed by a counter. This error signal, representing the degree of error in output signal of the delta-sigma modulator, is thus indicative of the modulator's operation. This particular testing scheme may be incorporated within the delta-sigma modulator itself to provide the modulator with a built-in self-test (BIST) capability. Brief Description of the Drawing FIG. 1 is a block schematic diagram of a preferred embodiment of the invention for testing a delta-sigma modulator. Detailed Description FIG. 1 is a block schematic diagram of a system 10, embodying the invention, for testing a delta-sigma modulator Analog-to-Digital (A/D) converter 12 and, particularly, its delta-sigma modulator 14. To best understand the operation of the system 10, a brief description of the structure and operation of the delta-sigma modulator A/D converter 12 will prove helpful. In its simplest form, the delta-sigma modulator A/D converter 12 comprises a delta-sigma modulator 14 for converting an input voltage to a binary (frequency) output signal and a digital filter 16 for filtering the output signal of the analog modulator. The delta-sigma modulator 14 may be represented as a differential amplifier 18 having an invert (-) input, and a non-invert input (+), the latter being supplied with an input signal V, corresponding to the input signal to the delta-sigma modulator. The differential amplifier 18 generates a signal, in accordance with the difference between the signals at its invert and non-invert inputs, which is supplied to the input of an integrator 20. The integrator 20 operates to integrate (that is, to sum and delay) the signal at its input, yielding an output signal which is supplied to the input of a comparator 22 which produces an output signal whose level is + b or -b volts (where b is typically unity) depending on whether the signal at the comparator input is greater or less than zero. The signal at the output of the comparator 22, which is the output signal of the analog modulator 14, is supplied to the invert input (-) of the differential amplifier 18. Thus, the output voltage of the comparator (+ b or - b volts) is subtracted by the differential amplifier 18 from the input voltage applied to its non-invert input (+). Depending on the magnitude of the input voltage V at its non-invert input, the differential amplifier 18 will output either a positive or negative voltage to the integrator 20 which sums the voltage input thereto with the voltage previously applied to the integrator input. The magnitude of the output voltage of the integrator 20 (which is dependent on the voltage output by the differential amplifier 18) controls whether the output signal of the comparator 22 is + b or - b volts. The process by which the delta-sigma modulator 14 operates is a dynamic one. The delta-sigma modulator 14 is responsive to a periodic timing or clock signal supplied from an external source (not shown). In response to a clock signal, the delta-sigma modulator 14 performs the steps of: (a) subtracting the comparator 22 output signal (+ b or - b ) from input signal V, (b) integrating the resultant voltage following subtraction, and (c) generating a signal of + b or - b depending on whether the voltage after integration is positive or negative. The resultant output signal of the comparator 22, (either +b or -b) is supplied to the digital filter 16 which filters the signal to generate a serial stream of bits representing the level of the input signal V. Testing of the delta-sigma modulator A/D converter 12, and, by implication, the delta-sigma modulator 14, can be carried out by establishing the error between the value of the input voltage V and the value of the digitized signal output by the filter 16. This may be accomplished by comparing the actual Signal-to-Noise (S/N) ratio of the delta-sigma modulator A/D converter 12 to a reference value representing the lowest allowable S/N ratio for the converter. In the past, the actual value of the S/N ratio of the delta-sigma modulator converter 12 was computed from a power spectrum density of the converter's output signals in a relatively complex manner. The delta-sigma modulator A/D converter 12 (that is, the combination of the delta-sigma modulator 14 and filter 16) is efficiently tested by the system 10 of FIG. 1, which serves to advantageously compute the S/N ratio of the device in the time domain. As shown in FIG. 1, the system 10 comprises a first Sample and Hold (S/H) device 24 of a well-known design for sampling a periodic input test signal at a first rate in excess of the Nyquist rate (i.e., twice the frequency of the signal), typically a preselected multiple of the Nyquist rate. Although not required, the input test signal is chosen to be sinusoidal. The sample of the input signal taken by the S/H device 24 is supplied to the input of the delta-sigma modulator 14 (i.e., the non-invert (+) input of the differential amplifier 18) each time the delta-sigma modulator is clocked. For each sample input to the delta-sigma modulator 14 in this fashion, the modulator generates an output signal , which is filtered by the filter 16. The output signal of the filter ( y '( k )) is indicative of the analog voltage of the sample of the signal input to the modulator. A second S/H device 26 is also supplied with the input signal and samples the signal at a second rate, typically the Nyquist rate. Thus, the S/H device 26 samples at a rate below the first sampling rate. The samples obtained by the S/H device 26, designated y ( k ), are input to a processor 28, such as a microprocessor or the like, which also receives the samples y '( k ) output by the filter 16 of the delta-sigma modulator A/D converter 12. It is not necessary to obtain the samples y ( k ) at the same time the samples y '( k ) are established by the delta-sigma modulator A/D converter 12. Rather, the samples y ( k ) could be obtained prior to obtaining the samples y '( k ) and stored for later use. The processor 28 serves to calculate the actual S/N ratio of the delta-sigma modulator A/D converter 12 by first computing a noise factor (intermediate error signal) e 2 in accordance with the formula: From the noise factor e 2 , the S/N ratio can be computed from the relationship where b is the magnitude of the output signal of the comparator 22 (typically unity). By comparing the S/N ratio computed from eq.(2) to the lowest allowable S/N value for the delta-sigma modulator A/D converter 12, any faults in the converter will manifest themselves. As may be appreciated, the instant testing technique will reveal if the delta-sigma modulator A/D converter 12 is operating properly. Correct operation of the delta-sigma modulator A/D converter 12 depends on proper operation of the delta-sigma modulator 14. Thus, the present technique tests the delta-sigma modulator 14. The advantage to testing the delta-sigma modulator converter 12 and, hence, the delta-sigma modulator 14 in the manner described above is that the complexity (i.e., the number of operations needed to obtain the S/N ratio) is on the order of n real multiplications and 2 n real additions in comparison to the prior art approach which generally has a complexity of n log ( n ) +2 n complex multiplications and n real additions. Not only is the complexity of testing reduced by the above-described technique, but the time required for testing is reduced since fewer operations need to be performed. The foregoing discloses a technique for verifying the operation of a delta-sigma modulator 14 in accordance with the difference between the modulator output signal when a sample from an input signal is obtained by sampling at a first rate, and a corresponding sample of the signal itself is obtained by sampling the signal at a second rate. It is to be understood that the above-described embodiments are merely illustrative of the invention. Various modifications and changes may be made thereto by those skilled in the art.

Claims: A method for testing a delta-sigma modulator (14) which serves to convert an analog input signal to a digital output signal, comprising the steps of: sampling an input test signal at a first rate and supplying each successive sample to the delta-sigma modulator (14) which, in turn, produces an output signal in accordance with the sample; CHARACTERISED BY sampling the input test signal at a second rate; generating an error signal in accordance with the difference between the value of the output signal generated by the delta-sigma modulator in response to each sample obtained at the first sampling rate, and the value of each sample obtained at the second sampling rate; and comparing the error signal to a preselected value, representing the value of the error signal when the delta-sigma modulator is operating properly. A method according to claim 1 further comprising the step of computing the signal-to-noise ratio of the delta-sigma modulator which is computed in accordance with the formula: S/N is the signal-to-noise ratio, b 2 is the square of the magnitude of the delta-sigma modulator output signal; and e 2 is an intermediate error signal given by: y '( k ) is the value of the delta-sigma modulator output signal for a successive sample obtained at the first rate, and y ( k ) is the value of a sample obtained at the second rate. A method according to claim 2 wherein: (a) the input signal has a preselected frequency; (b) the second sampling rate is chosen to be the Nyquist rate for the input signal; and (c) the first sampling rate is chosen to be a preselected multiple of the Nyquist rate. Apparatus for testing a delta-sigma modulator (14) comprising: first means (24) for sampling an input test signal at a first rate and for supplying the samples to the delta-sigma modulator; CHARACTERISED BY second means (26) for sampling the input signal at a second rate; and processor means (28) coupled to the second sampling means and the delta-sigma modulator (14) for generating an error signal in accordance with the difference between the value of the delta-sigma modulator output signal for each sample, and the value of a sample of the signal itself obtained from the second sampling means, and for establishing that the delta-sigma modulator is operating properly in accordance with the difference between the error signal and a prescribed value therefor. The apparatus according to claim 4 wherein the first sampling means (24) is a sample and hold device which samples the input signal at a rate greater than the Nyquist rate for the input signal. The apparatus according to claim 4 wherein the second sampling means (26) is a sample and hold device which samples the input signal at the Nyquist rate for the input signal.

Inventors: TSAI SHENG-JEN, TSAI, SHENG-JEN
Applicants: AT & T CORP, AT&T CORP.
Application year: 1991
Main classification: H03M1
IPC codes: G01R31, H03M1, H03M3, G01R29