ON THE INFLUENCE OF AMPLITUDE-PHASE ERRORS OF SINGLE-CHANNEL PATHS ON MEASUREMENT ACCURACY IN CERTAIN DIGITAL PHASE METER CIRCUITS

A. A. SHIBAEV

(Submitted by the scientific seminar of the Department of Theoretical Foundations of Radio Engineering, TIRiET)

The single-channel construction of the converter, the use of “phaseless” limiters, and the use of digital indication make it possible to expand the dynamic range of a phase meter to 60–80 dB. An estimate is made of the measurement error due to amplitude-phase errors of limiters over the dynamic range in three variants of phase-meter construction.

The desire to expand the dynamic range of the signals measured by phase-measuring apparatus is caused by the following reasons:

1. The need, in a number of practical cases, to measure “dynamic” phase characteristics of the systems under study (in those cases when the levels of the input signals change so rapidly that there is no operational possibility, in a short time, of bringing the instrument into its working state).

2. The possibility of increasing labor productivity, since the need for any additional adjustments at different levels of the measured signals is eliminated and, consequently, measurements can be performed at a faster rate.

Serially produced domestic phase meters F2-3, F2-4, F2-6, F2-7 require careful equalization of the signal levels at their inputs before measurements; moreover, the error of the given measurement depends substantially on the accuracy of this operation.

In [1] a frequency converter of a phase meter is described that has a dynamic range, for different ratios of input signals, of about 30 dB; for such a circuit this is the limiting value, determined by the dynamic range of the output level limiter, which, as shown, practically cannot exceed 80–90 dB.

The use of the principle of an entirely single-channel construction of the frequency converter (with switching of the input signals directly at the high frequency), the use of “phaseless” limiters at the converter output, and digital indication open up the possibility of constructing phase meters with a dynamic range of 60–80 dB without making additional adjustments.

Some of the possible variants (Figs. 1, 2, 3) of constructing frequency converters with processing of the measured phase shifts by means of a digital indicator are considered below.

In Figs. 1, 2, and 3 the following designations are used: 1 — commutator; 2, 3 — mixers; 4, 5 — intermediate-frequency filters; 6, 7 — “phaseless” limi-

paths; 8 — reversible digital indicator; 9 — tunable heterodyne; 10 — heterodyne AFC system; 11 — nonreversible digital indicator. The “phaseless” limiters 6 and 7 provide the specified

Fig. 1. Functional diagram of a phase meter with cross switching

Fig. 2. Functional diagram of a phase meter with double cross switching

Fig. 3. Functional diagram of a phase meter with switching in one channel

dynamic range of the phase meter and are multistage amplifiers with a linear-flat amplitude characteristic.

Several methods are known for forming such an amplitude characteristic; among the most effective of them may be classed auto-

...automatic gain control by changing the operating mode of the stages or by means of negative feedback, nonlinear shunting of the stage loads [2], and the use of nonlinear four-terminal networks as interstage couplings [3].

The phase errors that inevitably arise during operation of the limiter over a wide dynamic range, in the circuits under consideration, limit the accuracy of the phase meter, since they enter directly into the measurement error. As experiments, including those carried out by the author, show, depending on the operating frequency, gain factor, method of forming the required amplitude characteristic, the principle by which the trigger pulses for the digital indicator are formed from the limiter output voltage, and many other factors, the amplitude-phase error may have a monotonic (Fig. 4, a) or oscillatory character (Fig. 4, b). From the standpoint of the greatest error introduced into the measurement, the worst case, as is shown below, is the case of an oscillatory amplitude-phase error of the limiter.

Without touching on questions related to minimizing the amplitude-phase errors of limiters, let us estimate the errors they introduce into the measurement in the variants of phase-meter construction under consideration.

Figure 1 shows a functional diagram of a phase meter with cross commutation and with indication of the phase difference by means of a reversible digital indicator.

The single-channel construction of the converter eliminates frequency-phase errors of the path, as well as slow phase drifts arising from changes in climatic conditions and aging of circuit elements.

The nonlinear error arising from mutual leakage of the signals of the upper and lower channels through the switch circuits, in the system of mixers 2 and 3, through the power-supply circuits, and due to electromagnetic pickup, can be reduced (in the most unfavorable case, with a difference of input levels of 40–50 dB at frequencies not exceeding 100 MHz) to a value of less than 0.5–1°.

The error due to amplitude-phase errors of the limiters of the upper and lower channels can be estimated on the basis of the following reasoning. Let, in the first half-period of commutation, voltages \(U_1\) and \(U_2\), respectively, with initial phases \(\varphi_1\) and \(\varphi_2\), act at the inputs of limiters 6 and 7. Denoting the phase errors of the limiters in this case respectively by \(\Delta\varphi'_1\) and \(\Delta\varphi'_2\), we obtain the phase difference recorded in the digital indicator in the form

\[ \varphi_{\mathrm{I}} = (\varphi_1 - \varphi_2) + (\Delta\varphi'_1 - \Delta\varphi'_2). \tag{1} \]

If, in a first approximation, mixers 2 and 3 are regarded as linear over the dynamic range of input signals and as introducing no phase errors, then in the second half-period of commutation voltages \(U_2\) and \(U_1\), respectively, with initial phases \(\varphi_2\) and \(\varphi_1\), will act at the inputs of limiters 6 and 7. Denoting the phase errors of the limiters in this case by \(\Delta\varphi'_2\) and \(\Delta\varphi'_1\), we obtain the phase difference between the signals in the form

\[ \varphi_{\mathrm{II}} = (\varphi_2 - \varphi_1) + (\Delta\varphi'_2 - \Delta\varphi'_1). \tag{2} \]

The readings of the reversible digital indicator over a measurement cycle are

\[ \varphi = \varphi_{\mathrm{I}} - \varphi_{\mathrm{II}} = 2(\varphi_1 - \varphi_2) + (\Delta\varphi'_1 - \Delta\varphi'_2) + (\Delta\varphi'_1 - \Delta\varphi'_2). \tag{3} \]

It is not difficult to verify that, for a monotonic amplitude-phase error of the limiters (Fig. 4, a), the greatest possible error in the dynamic range is equal...

Fig. 4. Possible character of amplitude-phase errors of channel limiters:
a — monotonic characteristic; b, c — identical oscillating characteristics of the channels; b, d — “opposite-polarity” characteristics of the channels; b, e — mutually shifted characteristics of the channels.

\[ \Delta\varphi = |\Delta\varphi'_2+\Delta\varphi''_2|. \tag{4} \]

Here and below, for definiteness it is assumed that \(U_2>U_1\). With an oscillatory character of the error of the limiters in the dynamic range (Fig. 4, б), an error is introduced into the measurement, determined by the expression

\[ \Delta\varphi = |\Delta\varphi'_1+\Delta\varphi'_2+\Delta\varphi''_1+\Delta\varphi''_2|. \tag{4} \]

For identical amplitude–phase characteristics of the limiters (Fig. 4, б, в, \(\Delta\varphi'_1=\Delta\varphi''_1=\Delta\varphi_1;\ \Delta\varphi'_2=\Delta\varphi''_2=\Delta\varphi_2\)) the error has the greatest value

\[ \Delta\varphi = 2|\Delta\varphi_1+\Delta\varphi_2|. \tag{5} \]

In order to reduce the measurement error for the method under consideration of constructing the frequency converter, one should strive to obtain identical but “oppositely polarized” amplitude–phase characteristics of the limiters (Fig. 4, б, г); in this case the resulting error is

\[ \Delta\varphi = 0. \tag{6} \]

If it is impossible to ensure such a character of the amplitude–phase characteristics, then at least one of them should be “shifted” relative to the other in such a way that the maximum of one falls on the minimum of the other, and vice versa (Fig. 4, б, д); in this case

\[ \Delta\varphi = |\Delta\varphi_1+\Delta\varphi_2|. \tag{7} \]

In the case where the digital indicator implements the capability of the described converter to double, during a measurement cycle, the value of the phase difference of the signals under investigation (3), the errors are equal to those indicated above; but if the readings are recalculated by a factor of two, then the errors will, correspondingly, be two times smaller.

Figure 2 shows a functional diagram of a phase meter similar to the preceding one, but with the addition of a second switching stage directly at the input of the digital non-reversible indicator. In this case two modes of channel switching are possible. The commutators may operate in agreement or in opposition (in Fig. 2, respectively, \(aaa'a'\) and \(bbb'b'\), or \(aab'b'\) and \(bba'a'\)). In the first case the digital indicator records, over a measurement cycle, the count

\[ \varphi = \varphi_{\mathrm{I}}+\varphi_{\mathrm{II}} = 2(\varphi_1-\varphi_2)+(\Delta\varphi'_1-\Delta\varphi'_2)+(\Delta\varphi''_1-\Delta\varphi''_2), \tag{8} \]

as is evident, this expression corresponds to (3).

In the second case the indicator readings will be

\[ \varphi = \varphi_{\mathrm{I}}+\varphi_{\mathrm{II}} = 2(\varphi_2-\varphi_1)+(\Delta\varphi'_2-\Delta\varphi'_1)+(\Delta\varphi''_2-\Delta\varphi''_1), \tag{8′} \]

i.e., the sign of the measured phase difference changes to the opposite one. The conclusions drawn earlier concerning the character of the error due to the limiters are also valid for this case. The second cross-switching of the channels at the output of the frequency converter is not difficult to carry out, since the frequency of the switched signals lies within the range \(2 \div 20\) kHz.

Thus, the use of double commutation preserves all the advantages of the single-channel construction of the phase meter and makes it possible to substantially simplify the digital indicator, since there is no need to reverse the counter within the measurement cycle. Owing to the elimination of reversal, the capacity of the counter is reduced by approximately 30%, and, consequently, the reliability of its operation is increased.

In the functional diagram (Fig. 3), the lower channel serves as the reference channel, while sequential switching is performed in the upper channel; in this case the reading of the digital indicator over the measurement cycle is

\[ \varphi=\varphi_{\mathrm{I}}-\varphi_{\mathrm{II}}=(\varphi_1-\varphi_2)+(\Delta\varphi'_1-\Delta\varphi'_2). \tag{9} \]

In this case the amplitude-phase error of the limiter of the reference channel is eliminated, and only the error of the limiter of the common channel is determining. As the limiter of the reference channel, any limiter may be used that ensures formation of the start pulse for the digital indicator.

In addition to the errors introduced by the limiters, it is also necessary to take into account the amplitude-phase errors of the mixers and channels, which arise over a wide dynamic range of signals in their input circuits under overloads and due to an increase in the level of higher combination components of the intermediate frequency [4].

Everything said about the influence of the amplitude-phase errors of the limiters in the circuits considered on the measurement accuracy is also fully applicable to the errors introduced by mixers 2 and 3.

Summing up, it may be said that, in order to reduce the measurement error of the phase meter, one should strive, where possible, to obtain mutually opposite amplitude-phase characteristics of the channels in the circuits of Figs. 1 and 2, since in this case the digital indicator compensates them. In the circuit of Fig. 3 such compensation is absent. The upper limiting frequency for phase meters implemented according to the circuits considered is on the order of 100 MHz, since at higher frequencies interchannel parasitic couplings increase substantially.

REFERENCES

1. A. A. Shibaev, N. N. Shtarev. Range phase meter. Proceedings of the scientific-technical conference dedicated to Radio Day. Tomsk University Press, Tomsk, 1966.

2. V. F. Volkov. Logarithmic Amplifiers. State Technical Publishing House of the Ukrainian SSR, Kiev, 1962.

3. I. A. Volynchuk. On a gain-control system with small phase shifts in transistor amplifiers. Problems of Radio Electronics, Series XII, issue 28, 1966.

4. B. A. Khanov. On the spectrum of a signal subjected to frequency conversion. Elektrosvyaz, No. 10, 1960.