PHASE FREQUENCY RESPONSE MEASUREMENT METHOD

Abstract

A measurement of phase frequency response of a device under test (DUT), wherein the DUT is characterized by a set of switchable configurations, comprises choosing the steps of a particular configuration of the DUT having nominal parameters as a reference configuration, measuring an amplitude frequency response A.sub.ref (f) and a phase frequency response ϕ.sub.ref(f) of the reference configuration, processing all configurations of the DUT which are different from the reference configuration, one after another, by measuring an amplitude response A(f) of the configuration being processed, calculating a minimum phase difference response Δϕ.sub.min (f); and calculating for each configuration, a phase frequency response ϕ(f) of the respective configuration which is being processed, in accordance with ϕ(f) =ϕ.sub.ref(f)+Δϕ.sub.min(f).

Claims

1. A method of determining a phase frequency response for a device under test (DUT), wherein the DUT is characterized by a set of n switchable configurations, wherein n≥2, and each configuration is characterized by at least one minimum-phase component and zero, one or more non-minimum-phase components, said method comprising the steps of: by a processor/controller: A. establishing a particular configuration of the DUT having nominal parameters as a reference configuration; B. determining an amplitude frequency response A.sub.ref (f) and a phase frequency response ϕ.sub.ref(f) of the reference configuration; C. processing all of the remaining n−1 configurations of the DUT which are different from the reference configuration, one after another, by determining an amplitude frequency response A(f) of each of the remaining n−1 configurations being processed; D. determining for each of the n−1 remaining configurations, a minimum phase difference response Δϕ.sub.min(f); and E. calculating determining for each of the n−1 remaining configurations, a phase frequency response ϕ(f) of the respective configurations being processed, in accordance with ϕ(f)=ϕ.sub.ref(f)+Δϕ.sub.min(f); whereby the determined phase frequency responses ϕ(f) for the n configurations are representative of the phase frequency response determined for the DUT.

2. The method of claim 1, wherein said set of switchable configurations comprises a set of different input gain settings associated with each of the respective configurations of the DUT.

3. The method of claim 1, wherein the step of determining the minimum phase difference response Δϕ.sub.min(f) performed by the processor/controller, comprises the steps of: A. determining a minimum-phase ϕ.sub.rm.sub.e.sup.iof the reference configuration; B. calculating determining a minimum-phase ϕ.sup.min(f) of the configuration being processed; and C. determining the difference Δϕ.sub.min(f)=(ϕ.sup.min(f)−ϕ.sub.ref.sup.min(f)).

4. The method of claim 1, wherein the step of determining the minimum phase difference response Δϕ.sub.min(f) performed by the processor,/controller, comprises the steps of: for each of the n−1 remaining configurations as they are processed: A. determining an amplitude response ratio AR(f) of the amplitude frequency response A(f) of the configuration being processed to the reference amplitude frequency response Aref(f), where A.sub.R(f) =A(f)/A.sub.ref(f); and B. determining the minimum phase difference Δ.sub.min(f) of the amplitude response ratio A.sub.R (f).

Description

BRIEF DESCRIPTION OF THE DRAWINDS

[0012] FIG. 1 depicts measured amplitude frequency response of an exemplary DUT with two settings of input gain: =1 dB and −7 dB;

[0013] FIG. 2 illustrates phase frequency responses measured for two input gain settings of the DUT corresponding to the amplitude frequency responses shown in FIG. 1; and

[0014] FIG. 3 depicts a difference of the measured phase frequency responses of FIG. 2 and a corresponding difference calculated using a minimum-phase method of current disclosure.

DETAILED DESCRIPTION

[0015] According to the present disclosure, one configuration of a DUT is chosen as a reference configuration. Preferably, a reference configuration with a level of input signal which is close to an output level of the measuring device used to determine the phase frequency response. Such a choice makes it possible to measure for the reference configuration, not only an amplitude frequency response A.sub.f(f), but a phase frequency response ϕ.sub.ref(f) as well.

[0016] After the amplitude frequency response A.sub.ref(f), and the phase frequency response ϕ.sub.ref (f) of the reference configuration have been measured, the remaining DUT configurations are processed one after another. For each configuration to be processed, the amplitude frequency response A(f) is measured. The measured amplitude frequency response A(f) together with the frequency responses A.sub.ref(f), and ϕ.sub.ref (f) of the reference configuration, are used as initial data for calculation of the phase frequency response ϕ(f) of the configuration which is being processed. When for all configurations of DUT, the amplitude frequency response A(f) and the phase frequency response ϕ(f) are determined, the measurement is completed.

[0017] In the theory of electrical circuits, a gain-phase equation established by a Bode Plot, is well known. For a minimum-phase circuit with the complex frequency response {dot over (H)}(f), it relates the phase frequency response ϕ(f) =arg{H(f)} to its amplitude frequency response A(f) =|{dot over (H)}(f)|. Several versions of Bode Plots are possible. One of the versions allows simple implementation in a FPGA. It determines the phase frequency response ϕ(f) as a Hilbert transform of a logarithm of an amplitude frequency response In(A(f)) and consists of the following sequence of operations:

[0018] a. calculation of In(A(f));

[0019] b. calculation of a Fourier transform F(f) of In(A(f));

[0020] c. equating F(f) to zero at negative f:

[00001]$\begin{array}{cc}{F}_0\left(f\right)=\{\begin{array}{cc}F\left(f\right),& \mathrm{if}f\ge 0\\ 0& \mathrm{if}f<0\end{array};& \left(1\right)\end{array}$

[0021] d. determining ϕ(f) as an inverse Fourier transform of F.sub.0(f).

[0022] Direct attempts to determine the phase frequency response of a DUT, by determining a Bode plot for the measured amplitude frequency response, have been made. However, such attempts often have led to erroneous results. The explanation is simple enough: the common DUT is usually not a minimum-phase circuit.

[0023] In the case of an analog to digital converter (taken as an example), the front end comprises, along with other units, an anti-aliasing filter and cables connecting its different parts together. Such circuits are not “minimum-phase” by their nature. As the result, the front end of an ADC is not a minimum-phase circuit.

[0024] In accordance with the present disclosure, advantage is taken of the fact that the units which cause the not a minimum-phase character of the DUT, are common to the different DUT configurations. These units are not altered when switching from one DUT configuration to another is performed. Therefore, the minimum phase calculation applied to both DUT configurations, is expected to have identical non-minimum phase terms.

[0025] One approach to calculating a change of phase frequency response for different DUT configurations is based on estimating minimum phase terms for each configuration. First, a minimum phase part of the reference frequency response ϕ.sub.ref (f) is derermined . A calculation of a Hilbert transform requires a symmetrical extension (reflection) of a measured amplitude response up to a sampling frequency (twice the Nyquist frequency) corresponding to a property of a real-valued signal Fourier spectra. After this operation, the last point of a frequency response corresponds to a second measured frequency of A.sub.ref(f) (with a first (zero) frequency corresponding to DC). A Hilbert transform results in a minimum phase of reference system ϕ.sub.ref.sup.min(f). For determining the phase frequency response of a configuration which is different from reference configuration, a minimum phase calculation similar to that described above is repeated for the measured amplitude response A(f), and then a minimum phase ϕ.sup.min(f) for this configuration is determined.

[0026] A reference phase measurement ϕ.sub.ref(f) contains non-minimum phase terms corresponding to non-minimum ADC phase units, including an anti-aliasing filter, connecting cables and other elements. However, these parts do not change when a different configuration is used, e.g., for the case of a changing input attenuation. Therefore, a phase response corresponding to the changed configuration ϕ(f) can be obtained by adding a difference of minimum phase terms to the reference phase response:

ϕ(f)=ϕ.sub.ref(f)+(ϕ.sup.min(f)−ϕ.sub.ref.sup.min(f))=ϕ.sub.ref(f)+Δϕ.sub.min(f)  (2)

[0027] Another embodiment of this method can be realized by using a ratio of a measured amplitude frequency response to the reference configuration amplitude reference response: A.sub.R(f) =A(f)/A.sub.ref(f) . This amplitude response ratio can be represented as an absolute value of the complex frequency responses ratio having amplitude and phase terms:

[00002]$A_R\left(f\right)=.Math.\frac{H\left(f\right)}{H_{\mathrm{ref}}\left(f\right)}.Math.=.Math.\frac{A\left(f\right)e^{i\varphi \left(f\right)}}{A_{\mathrm{ref}}\left(f\right)e^{i{\varphi }_{\mathrm{ref}}\left(f\right)}}.Math.=.Math.\frac{A\left(f\right)}{A_{\mathrm{ref}}\left(f\right)}{e}^{i\left(\varphi \left(f\right)-{\varphi }_{\mathrm{ref}}\left(f\right)\right)}.Math.$

[0028] The complex frequency response of any configuration represents a product of amplitude and phase responses. Phase responses of reference and non-reference configurations comprise both minimum-phase and non-minimum-phase terms. Since non-minimum phase terms of both configurations are the same, they cancel out in the phase difference term, and, therefore, the phase of the amplitude ratio A.sub.R(f) contains exclusively minimum-phase terms.

[0029] The frequency response is symmetrically extended similarly to the procedure described above, and minimum phase Δϕ.sub.min is calculated by using a Hilbert transform. From the above equations, it follows that Δ.sub.min =ϕ.sup.min(f)−ϕ.sub.ref.sup.min(f)), and, therefore, Eq.(2) above can be used for a phase frequency response calculation.

[0030] Both embodiments of the described procedure were used for measurement of the Phase response of a 32 GS/s ADC using different input attenuation. The results are shown in FIGS. 1-3. FIGS. 1 and 2 depict amplitude and phase responses for two different ADC attenuation settings (−1 dB and −7 dB). A full frequency range phase response was measured in both settings for purpose of validation of the minimum phase response method. FIG. 3 shows a difference of phase responses between these gain settings. As shown, the phase deviation exceeds 10 degrees at 8 GHz and increases to 20 degrees around 12.5 GHz. The phase response for the gain setting of 7 dB using the reference phase response, and the minimum phase calculation is within a 2 degree range from the actual measurement. The small phase difference is due to small residual non-minimum phase components. The estimation of minimum phase results in an order of magnitude improvement of the phase estimation accuracy for the different input gains of ADC.

[0031] Therefore, the disclosed invention achieves a high accuracy of the phase frequency response measurement by utilizing a minimum-phase difference method. This method simplifies the measurement setup by using standard signal generating devices and provides considerable time gains for calibration of a device under test.

[0032] Although this invention has been described in terms of certain embodiments, other embodiments that are apparent to those of ordinary skill in the art, including embodiments which do not provide all the benefits and features set forth herein, are also within the scope of this invention. Accordingly, the scope of the present invention is defined only by reference to the appended claims.