GROUP DELAY MEASUREMENT APPARATUS AND METHOD

Abstract

Measurement of group delay for a device under test (DUT). A test signal includes (i) a low frequency sine wave f.sub.LF, (ii) sine wave harmonics at a high frequency f.sub.HF, (iii) L pairs of sideband components at frequencies k.Math.f.sub.HF2.Math.f.sub.LF, where k odd, and M pairs of sideband components at frequencies k.Math.f.sub.HFf.sub.LF, where k is even. At DUT output, (i) phase .sub.LF at frequency f.sub.LF is measured, (ii) both sideband phase .sub.right(k) at frequencies k.Math.f.sub.HF+2.Math.f.sub.LF and phase .sub.left(k) at frequencies k.Math.f.sub.HF2.Math.f.sub.LF for odd k, are measured, and (iii) both sideband phases .sub.right(k) at frequencies k.Math.f.sub.HF+f.sub.LF and .sub.left(k) at frequencies k.Math.f.sub.HFf.sub.LF for even k, are measured. Group delay .sub.k at frequencies k.Math.F.sub.HF, are determined from: .sub.k=(.sub.right(k).sub.left(k)4.Math..sub.L)/(4.Math.f.sub.LF) for k odd, and .sub.k=(.sub.right(k).sub.left(k)2.Math..sub.L)/(2.Math.f.sub.LF) for k even.

Claims

1. A method of group delay measurement for a device under test (DUT) having an input for receiving a signal characterized by a first domain, and an output for providing an output signal characterized by a second domain in response to the input signal received by the input, comprising the steps of: a. controlling a signal generator to generate a test signal, wherein the test signal includes as spectral components: i. a sine wave characterized by a relatively low frequency f.sub.LF; ii. a set of harmonics of a sine wave characterized by a relatively high frequency f.sub.HF; iii. a set of L pairs of sideband components characterized by frequencies k.Math.f.sub.HF2.Math.f.sub.LF, where k is an odd number; iv. a set of M pairs of sideband components characterized by frequencies k.Math.f.sub.HFf.sub.LF, where k is an even number; wherein phase .sub.right(k) of the sideband components with frequencies k.Math.f.sub.HF+n.Math.f.sub.LF, and phase .sub.left(k) of the sideband components with frequencies k.Math.f.sub.HFn.Math.f.sub.LF, are related to the phase .sub.LF of the component with frequency f.sub.LF and phase .sub.HF of the component with the frequency f.sub.HF, by equations
.sub.right=k.Math..sub.HF+n.Math..sub.LF,
.sub.left=k.Math..sub.HFn.Math..sub.LF. b. applying the test signal to the input of a device under test and c. obtaining from the output of the device under test, an output signal responsive to the test signal applied to the input with a phase measuring device by: i. measuring phase .sub.LF of a component thereof characterized by frequency f.sub.LF; ii. measuring the phase .sub.right(k) of sideband components thereof characterized by frequencies k.Math.f.sub.HF+2.Math.f.sub.LF and phase .sub.left(k) of sideband components with the frequencies k.Math.f.sub.HF2.Math.f.sub.LF for odd numbers k; and iii. measuring phases .sub.right(k) of the sideband components thereof characterized by frequencies k.Math.f.sub.HF+f.sub.LF and .sub.left(k) of the sideband components with the frequencies k.Math.f.sub.HFf.sub.LF for even numbers k; and d. analyzing the measured phases by: i. calculating with a digital processor, a group delay .sub.k at frequencies k.Math.F.sub.HF according to: .sub.k=(.sub.right(k).sub.left(k)4.Math..sub.LF)/(4.Math.f.sub.LF) where k is odd, and .sub.k=(.sub.right(k).sub.left(k)2.Math..sub.LF)/(2.Math.f.sub.LF) where k is even; and ii. determining with a digital processor, group delay for N frequencies in a range of interest by repeating N/(L+M) times, the set of steps a, . . . , c, each time for a value of the frequency f.sub.HF.

2. The method of group delay measurement according to claim 1, wherein the generating of the test signal is performed by producing two sine waves with respective frequencies f.sub.LF and f.sub.HF, summing the two sine waves, and amplitude limiting the resultant sum by applying the summed sine waves to than amplitude limiter.

3. The method of group delay measurement according to claim 2, wherein the measured phases of the spectral components of the output signal are determined by a digital processor calculating a Fast Fourier Transform (FFT) of the signal at the output of the device under test.

4. The method of group delay measurement according to claim 1, wherein the first domain includes frequencies in a first range, and the second domain includes frequencies in a second range.

5. The method of group delay measurement according to claim 4, wherein range of frequencies of the first domain is lower than the range of frequencies of the second domain.

6. The method of group delay measurement according to claim 4, wherein range of frequencies of the first domain is higher than the range of frequencies of the second.

7. The method of group delay measurement according to claim 1, wherein the first domain is an analog domain, and the second domain is a digital domain.

8. The method of group delay measurement according to claim 1, wherein the first domain is a digital domain, and the second domain is an analog domain.

9. An apparatus for group delay measurement for a device under test (DUT) having an input for receiving a signal characterized by a first domain, and an output for providing an output signal characterized by a second domain in response to the input signal received by the input, comprising: a. a first oscillator providing at an output, wherein the sine wave is characterized by a relatively low frequency f.sub.LF; b. a second oscillator providing at an output, wherein the sine wave is characterized by a relatively high frequency f.sub.HF; c. an amplitude limiter including a first input, a second input and an output, wherein the first input is connected to the output of the first oscillator, the second input is connected to the output of the second oscillator, and the output is connected to the input of a device under test, and wherein the amplitude limiter is configured to produce at the output thereof, a test signal corresponding to an amplitude limited sum of the inputs to the amplitude limiter, wherein the test signal includes as spectral components: i. a sine wave characterized by a relatively low frequency f.sub.LF; ii. a set of harmonics of a sine wave characterized by a relatively high frequency f.sub.HF; iii. a set of L pairs of sideband components characterized by frequencies k.Math.f.sub.HF2f.sub.LF, where k is an odd number; iv. a set of M pairs of sideband components characterized by frequencies k.Math.f.sub.HFf.sub.LF, where k is an even number; wherein phase .sub.right(k) of the sideband components with frequencies k.Math.f.sub.HF+n.Math.f.sub.LF, and phase .sub.left(k) of the sideband components with frequencies k.Math.f.sub.HFn.Math.f.sub.LF, are related to the phase .sub.LF of the component with frequency f.sub.LF and phase .sub.HF of the component with the frequency f.sub.HF, by equations
.sub.right=k.Math..sub.HF+n.Math..sub.LF,
.sub.left=k.Math..sub.HFn.Math..sub.LF.; d. a measurement unit having an input configured to receive a signal from the output of the device under test in a predetermined domain wherein the measurement unit includes a phase measuring device operative on the signal received from the output of the device under test for: i. measuring phase .sub.LF of a component thereof characterized by frequency f.sub.LF; ii. measuring the phase .sub.right(k) of sideband components thereof characterized by frequencies k.Math.f.sub.HF+2.Math.f.sub.LF and phase .sub.left(k) of sideband components with the frequencies k.Math.f.sub.HF2.Math.f.sub.LF for odd numbers k; and iii. measuring phases .sub.right(k) of the sideband components thereof characterized by frequencies k.Math.f.sub.HF+f.sub.LF and .sub.left(k) of the sideband components with the frequencies k.Math.f.sub.HFf.sub.LF for even numbers k; and e. a processing unit for analyzing the measured phases from the measurement unit, to determine a group delay for frequencies f.sub.LF and f.sub.HF for the device under test, by: calculating with a digital processor, a group delay .sub.k at frequencies k.Math.F.sub.HF according to: .sub.k=(.sub.right(k).sub.left(k)4.Math..sub.LF)/(4.Math.f.sub.LF) where k is odd, and .sub.k=(.sub.right(k).sub.left(k)2.Math..sub.LF)/(2.Math.f.sub.LF) where k is even; and f. an interface unit having an input connected to the output of the device under test and an output connected to the input of the processing unit, said interface unit being configured to provide the output of the device under test in the predetermined domain to the input of the processing unit; and g. a control unit configured to arrange measurement performance step by step, to establish the frequency f.sub.HF for each step of measurement and to determine group delay of the device under test for harmonics k.Math.f.sub.HF of the frequency f.sub.HF.

10. The apparatus for group delay measurement according to claim 9, wherein the processing unit determines phases of input signal spectral components by performing a Fast Fourier Transform (FFT) on the received signal.

11. The apparatus for group delay measurement according to claim 9, wherein the amplitude limiter includes an adder configured to receive the sine waves from the first oscillator and the second oscillator and provide at an output of the adder, a sum of the received sine waves, and provide at the output of the amplitude limiter, an amplitude limited form of the sum.

12. The apparatus for group delay measurement according to claim 9, wherein the amplitude limiter includes an amplifier with differential inputs configured to receive the sine waves from the first oscillator and the second oscillator, and to provide at an output of the amplitude limiter, an amplitude limited form of a sum of the signals at the differential inputs.

13. The apparatus for group delay measurement according to claim 9, wherein the device under test is an analog to digital converter.

14. The apparatus for group delay measurement according to claim 9, wherein the apparatus is configured to receive a digital frequency converter as a device under test.

15. The apparatus for group delay measurement according to claim 9, wherein the apparatus is configured to receive an analog device as a device under test.

16. The apparatus for group delay measurement according to claim 9, wherein the apparatus is configured to measure group delay of an analog up converter having an input and an output, as a device under test, and further comprising: an adder including: i. a first input configured to receive the sine wave characterized by a relatively low frequency f.sub.LF from the first oscillator, ii. a second input configured to receive the output of the device under test, and iii. an output coupled to the input of the processing unit, wherein the adder is configured to provide a sum of the sine wave at the first input and output of the analog up converter to the input of the processing unit.

17. The group delay measurement apparatus according to claim 9, wherein the first domain includes frequencies in a first range, and the second domain includes frequencies in a second range.

18. The group delay measurement apparatus according to claim 17, wherein range of frequencies of the first domain is lower than the range of frequencies of the second domain.

19. The group delay measurement apparatus according to claim 17, wherein range of frequencies of the first domain is higher than the range of frequencies of the second domain.

20. The group delay measurement apparatus according to claim 9, wherein the first domain is an analog domain, and the second domain is a digital domain.

21. The group delay measurement apparatus according to claim 9, wherein the first domain is a digital domain, and the second domain is an analog domain.

22. The method of group delay measurement according to claim 2, wherein the producing of each of the two sine waves is performed by an oscillator.

23. The method of group delay measurement according to claim 2, wherein the summing of the two sine waves is performed by an adder.

24. The method of group delay measurement according to claim 2, wherein the summing of the two sine waves and amplitude limiting is performed by applying the two sine waves to differential inputs of a limiting amplifier.

Description

BRIEF DESCRIPTION OF THE DRAWINGS

[0015] FIG. 1 depicts a method for generating components of a signal spectrum using a mixer for use in a prior art group delay measurement system;

[0016] FIG. 2 depicts a block diagram of prior art group delay measurement system using separate reference and measurement signal paths;

[0017] FIG. 3 shows a block diagram of an exemplary group delay measurement system according to the current technology;

[0018] FIG. 4a shows an exemplary amplitude limiter of the configuration of FIG. 3, configured as a cascade connection of an adder and an amplitude limiter;

[0019] FIG. 4b shows an exemplary amplitude limiter of the configuration of FIG. 3, configured as a limiting amplifier;

[0020] FIG. 5a illustrates an exemplary waveform at the output of an amplitude limiter in a form of the technology;

[0021] FIG. 5b illustrates an exemplary spectrum at the output of an amplitude limiter in a form of the technology;

[0022] FIG. 6 shows a block diagram of group delay measurement configuration for an analog up converter according to the technology;

[0023] FIG. 7a illustrate results of a numerical simulation of the method of technology for an experimental group delay measurement of a 40 Gs/s ADC; and

[0024] FIG. 7b shows a zoomed region of FIG. 7a in the range 10700 to 13300 MHz.

DETAILED DESCRIPTION

[0025] A block diagram of an exemplary apparatus for group delay measurement, according to the current technology, is shown in FIG. 3. The apparatus comprises two sine wave oscillators: a low frequency sine wave oscillator 1, generating a low frequency f.sub.LF, and a high frequency sine wave oscillator 2, generating a high frequency f.sub.HF. Output signals of oscillators 1 and 2 are connected to the inputs of an amplitude limiter 3. A signal formed in amplitude limiter 3 is applied to an input of a DUT 4. A signal from an output of DUT 4 is processed in a processing unit 6. An interface unit 5 is coupled between the output of DUT 4 and an input of processing unit 6. The interface unit 5 converts the signal from the output of DUT 4 into a form that matches the input of processing unit 6.

[0026] A control unit 7 manages the process of measurement step by step, establishing a frequency f.sub.HF for each step of measurement, and determining group delay of DUT 4 for harmonics k.Math.f.sub.HF of the frequency f.sub.HF that had been set.

[0027] The amplitude limiter 3 may be constructed as a cascade connection of an adder with a limiting amplifier (for example, as shown in FIG. 4a), or as a limiting amplifier with a differential input (for example, as shown in FIG. 4b). In both cases, the formed test signal presents a limited sum of two sine waves.

[0028] A signal at the output of amplitude limiter 3 is shown in FIG. 5a, where, as an example, a mix of two sine waves is amplitude limited at a threshold level of 10% from the original amplitude. A sum of the low and high frequency signals at the output of the amplitude limiter 3 is transformed into a sequence of width modulated pulses. During a positive half period of the low frequency, those pulses have narrower negative-going, and wider positive-going, widths. During negative half period, the negative-going polarity pulses are wider, and the positive-going polarity pulses are narrower. This pulse width modulation is periodic, with the period of low frequency signal. As a result, a low frequency component at f.sub.LF is present at the output of amplitude limiter 3, with the phase of this low frequency signal being equal the phase of original low frequency sine wave.

[0029] The relationship between the voltage at the output of the amplitude limiter, and the voltage at its input, may be approximated by a Taylor series decomposition having odd components, i.e., by a polynomial of the form ax+bx.sup.3+cx.sup.5. . . . As a result, the spectrum of the signal at the output of amplitude limiter 3 comprises multiple combination frequencies k.Math.f.sub.HFn.Math.f.sub.LF, where k, n are integers and k+n is an odd number. An illustrative example of the spectrum at the output of the amplitude limiter 3 for f.sub.LF=25 MHz, f.sub.HF=150 MHz, is shown in FIG. 5b. The main spectral peak corresponds to the first harmonic of the high frequency sine wave; the magnitude spectrum is normalized to 0 dB at f.sub.HF=150 MHz. As seen, the spectrum has distinct low frequency spectral component at 25 MHz, and a number of combination frequencies (sidebands). The highest sideband magnitude is around second harmonic of the high frequency signal, i.e., at 2.Math.f.sub.HFf.sub.LF, with 10 dB magnitude. The dominance of sidebands at the second harmonic is explained by the fact that the signal consists of a sequence of width-modulated rectangular pulses. It is well known that asymmetry of pulse period generates even signal harmonics while a perfectly symmetrical pulse train has only odd harmonics. The asymmetry of modulated pulses is opposite for positive and negative half periods of the low frequency signal. Therefore, the average asymmetry over a full period of the low frequency signal is zero and the second harmonic of the high frequency signal is not present. However, modulation of pulse width asymmetry with frequency f.sub.LF causes an appearance of sidebands around a second harmonic at 2.Math.f.sub.HFf.sub.LF. Weaker sidebands are also present at the fourth harmonic 4.Math.f.sub.HFf.sub.LF; second-order sidebands are present at f.sub.HF2.Math.F.sub.LF and 3.Math.f.sub.HF2.Math.f.sub.LF. All sideband pairs can be used for phase and group delay measurements. The sidebands at the second harmonic of the high frequency signal are preferable due to stronger spectral magnitude and better signal-to-noise ratio.

[0030] DUT 4 may be an ADC, for which group delay is to be measured. Alternatively, DUT 4 may be a digital frequency converter with an ADC as the converter component. The current technology makes it possible to measure group delay of analog devices as well. In such cases, an ADC is incorporated in the interface unit 5. In any event, the signal at the input of the processing unit 6 always has a digital form.

[0031] In a form, when the technology is used for group delay measurement of an analog up-converter, measures should be used to ensure presence of the component with the frequency f.sub.LF in the spectrum of the signal at output of the DUT 4. An exemplary block diagram for this form is shown in FIG. 6. In this block diagram, DUT 4 has an additional input 10 connected to the output of the low frequency oscillator 1. Inside the DUT 4, an adder 9 is coupled between an analog up-converter 8 and the output of the DUT 4. The additional input 10 of DUT 4 is connected to a first input of the adder 9. A second input of adder 9 is connected to an output of analog up-converter 8. The sine wave with frequency f.sub.LF produced by the oscillator 1, is applied by way of additional input 10 of DUT 4 to the first input of adder 9. In adder 9, the sine wave of the frequency f.sub.LF is mixed with the output signal of analog up-converter 8, and as a part of the mixed signal passes to the output of DUT 4. The availability of the sine wave of the frequency f.sub.LF at the input of the processing unit 5 makes possible the measurement of the group delay of the analog up-converter 8 in accordance with the technology.

[0032] The signal coming applied to the input of the processing unit 6 may be Fourier transformed, resulting in a complex Fourier spectrum. This operation can be performed using an FPGA, a computer or a dedicated digital processor. Thus, phases of all spectrum components can be obtained from a single Fourier transform. By sweeping the high frequency signal f.sub.HF in a band of interest, phase measurements can be obtained for a range of frequencies.

[0033] In explanation, DUT 4 has a phase frequency response .sub.DUT(f), so that a sine wave with the frequency f passing through DUT 4, experiences a phase shift .sub.DUT(f). At the input of DUT 4, the right sideband for the harmonic number k of the high frequency f.sub.HF, has a frequency=k.Math.f.sub.HF+n.Math.f.sub.LF and a phase .sub.right=k.Math..sub.HF+n.Math..sub.LF, where .sub.HF and .sub.LF are the phases of the sine waves with the frequencies f.sub.HF and f.sub.LF, respectively. After passing through DUT 4, the phase becomes .sub.right=k.Math..sub.HF+n.Math..sub.LF+.sub.DUT(k.Math.f.sub.HF+n.Math.f.sub.LF). The left sideband for the harmonic number k of the high frequency f.sub.HF at the output of DUT 4 has a frequency k.Math.f.sub.HFn.Math.f.sub.LF and a phase .sub.left=k.Math..sub.HFn.Math..sub.LF+.sub.DUT(k.Math.f.sub.HFn.Math.f.sub.LF). The phases .sub.HF and .sub.LF of high and low frequency sine wave oscillators are unknown and different during each signal acquisition. However, the high frequency phase is identical for the right and left sidebands, and therefore the phase difference equals =.sub.right.sub.left=.sub.DUT(k.Math.f.sub.HF+n.Math.f.sub.LF).sub.DUT(k.Math.f.sub.HFn.Math.f.sub.LF)+2.Math.n.Math..sub.LF..

[0034] The low frequency phase .sub.LF creates a shift of measured value , wherein this shift is different for each signal acquisition. However, since the low frequency component is always present in the signal spectrum, the value of .sub.LF is measured from the signal spectrum and compensated. After this operation, the group delay value is calculated as =/(f.sub.rightf.sub.left)/(2.Math.)=/(2.Math.n.Math.f.sub.LF)/(2.Math.). Thus, group delay values are obtained for arbitrary frequency with arbitrary frequency steps, depending on a particular choice of f.sub.HF and f.sub.LF. By choosing small value of the low frequency (e.g., 2-5 MHz), any monotonic and slow changing group delay introduced by the limiter circuit is minimized, while group delay of DUT 4 is obtained with high frequency resolution and accuracy.

[0035] The method of current technology can be readily simulated using an idealized amplitude limiter and a 40 Gs/s ADC model. In the simulation, the ADC is modeled using real phase and amplitude frequency responses. A test signal is obtained by mixing a variable high frequency signal in the range of 100 MHz-13 GHz with a 50 MHz step, using a 5 MHz low frequency signal. Both high and low frequency signals are assigned random phase values for each frequency in the measurement range. The sum of the sine waves is amplitude limited and each spectral component is distorted by the frequency response functions of the ADC. When the received signal is mixed with additive white Gaussian noise at 40 dB SNR, the spectrum of the signal is determined using a Fast Fourier transform and group delay is calculated as (f)=(2.Math.n.sub.LF)/(2.Math.n.Math.f.sub.LF)/(2.Math.). The result of this simulation using multiple independent measurements coincides with a model group delay within 5 ps accuracy. Different distortions of the amplitude limiter circuit are also modeled, such as asymmetry of positive and negative threshold levels, monotonic group delay and frequency roll-off. None of them degraded measured group delay.

[0036] FIGS. 7a and 7b show results of an experimental measurement of a group delay of 40 Gs/s for an interleaved ADC using several independent acquisition sets with different values of low frequency (2.5, 5, 10 and 20 MHz). Each measurement set consisted of a single low frequency value and 640 high frequency values in the range of 20 to 14000 MHz with 21.925 MHz steps. Each digitized waveform size is set at 8 million samples in order to provide sufficient data averaging and high resolution spectral measurement. As seen from FIG. 7a, all data sets result in practically identical measurements of group delay. FIG. 7b shows a zoomed region of FIG. 7a in the range 10700 to 13300 MHz, demonstrating that different low frequency signals (2.5 to 20 MHz) result in nearly identical group delay values, with a maximum deviation less than 10 ps, this accuracy in highly non-uniform high frequency region, is sufficient for all practical purposes.

[0037] Although the foregoing description of the embodiment of the present technology contains some details for purposes of clarity of understanding, the technology is not limited to the detail provided. There are many alternative ways of implementing the technology. The disclosed embodiments are illustrative and not restrictive.