FREQUENCY ERROR OF A PHOTOELECTRIC COMPARATOR IN MEASUREMENTS OF VOLTAGES GREATER THAN THE RATED VOLTAGE OF AN INCANDESCENT LAMP

Yu. M. FOMICHEV

(Presented by the scientific seminar of the Department of Radio Engineering)

When comparing alternating voltages whose rms value exceeds the rated value for an incandescent lamp (IL), an additional resistance \(R_g\) is inserted in series with the latter. Its magnitude is determined by the limits of the measured voltage and by the position of the lamp operating point. Obviously, in this case the comparison error (in the high-frequency region) will be affected both by the reactances of the IL and by those of the additional resistance. Moreover, in constructing such a converter, the question also arises of the place at which the IL is to be connected.

As was noted in [1], the input circuit of the converter must be regarded as a nonuniform long line short-circuited at the end*). In view of the complexity of analyzing a nonuniform long line with more than two sections, we shall represent the input circuit of the converter in the form of three sections of a lossless line, two of which are loaded by four-terminal networks \(\dot K_1\) and \(\dot K_2\), while the third is short-circuited (Fig. 1). The four-terminal networks \(\dot K_1\) and \(\dot K_2\) replace the additional resistance and the incandescent body of the lamp.

Fig. 1

Solving the wave equations for the currents flowing through the four-terminal networks gives the following results:

*) Usually the input circuit of electrothermal converters is regarded as a uniform long line loaded by the active resistance of the heater [2, 3], and the comparison error is calculated through the input resistance of the line. Such a representation is not entirely complete, since in this case the high-frequency component of the error due to the nonuniformity of the current distribution along the length of the converter is not taken into account.

\[ |\dot I_4|=\frac{|\dot U|\cos\gamma l_3}{|z|}; \]

\[ |\dot I_2|=|\dot I_4|\cdot \sqrt{ \left[\cos\gamma l_2+\frac{\omega L_{\text{l}}}{z_0}\sin\gamma l_2-\tg\gamma l_3\cdot\sin\gamma l_2\right]^2 + \left[\frac{R_{\text{l}}}{z_0}\sin\gamma l_2\right]^2 } \approx \]

\[ \approx \frac{|\dot U|\cos\gamma l_3\cdot\cos\gamma l_2}{|Z|}, \]

where

\[ |\dot Z|= \sqrt{ \left[ R_{\text{l}}ACE+R_gE\left(AC-BD+\omega L_{\text{l}}A\frac{D}{Z_0}\right)+ \right. } \]

\[ \left. +\left[(\omega L_{\text{l}}AC-BC-AD)E+(\omega L_gE-Z_0F)\left(AC-BD+ \right.\right. \]

\[ \left.\left. +R_{\text{l}}\frac{D}{Z_0}A(\omega L_gE-Z_0F)\right)\right]^2+ \right. \]

\[ \left. +\omega L_{\text{l}}A)\frac{D}{Z_0}-R_gR_{\text{l}}\frac{D}{Z_0}AE \right]^2 }; \]

\[ A=\cos\gamma l_3;\quad B=\sin\gamma l_3;\quad C=\cos\gamma l_2;\quad D=\sin\gamma l_2; \]

\[ E=\cos\gamma l_1;\quad F=\sin\gamma l_1; \]

— \(L_g\) is the inductance of the added resistance,
\(Z_0\) is the characteristic impedance of the lossless line.

Starting from the relations obtained and formula (3) from [1], one can write the general expression for the current flowing at any point of the input circuit of the transducer

\[ [\,\dot I_{n\xi}\,]\approx \frac{|\dot U_{\text{in}}|\cdot\cos\gamma_n\cdot\xi_n \prod_{i=1}^{n}\cos\gamma_i\cdot l_i}{|Z|}, \tag{1} \]

where \(\gamma_i, l_i\) are the propagation constants and lengths of the \(i\)-th homogeneous sections of the line situated between its end and the section in which the current is determined;

\(I_{n\xi}\) is the magnitude of the current in any section of the line;

\(\gamma_n,\xi_n\) are the propagation constant and the current coordinate of the section of the line in which the current is determined;

\(|Z|\) is the magnitude of the total impedance of the circuit.

Analyzing the expression obtained, it is not difficult to conclude that the smallest comparison error will occur for \(l_i=0\) and \(\xi_n\to0\), i.e., when the IL is connected closer to the short-circuited end of the transducer.

Using the effect of the nonuniform distribution of current along the length of the transducer, the transducer can be adjusted to the minimum of \(\delta_f\) by changing the distance between the IL and the short-circuited end of the transducer.

The conclusions drawn were verified experimentally. For this purpose a photoelectric transducer was developed in the form of a light-tight section of coaxial line, the central conductor of which consisted of two ILs connected in series, and it was possible to change the distance between one of the lamps and the short-circuited end of the transducer (Fig. 2). Each lamp illuminated one of two photoresistors connected in the arms of different bridges (Fig. 3a). The bridges were balanced when a dc voltage was applied to the ILs (from source 2, Fig. 3a). Then, to the input of the transducer was appli-

an alternating voltage was applied, the value of which was set according to the zero readings of the null indicator first of one bridge, and then of the other bridge. The input voltage was measured with a V3-24 voltmeter. The difference between the readings of the V3-24 is about 3% at 100 MHz,

Fig. 2

with the larger voltage value being set according to the incandescent lamp (IL) (Fig. 3a). The relative dependence of the set voltage value on the distance between the IL and the short-circuiting piston is shown in Fig. 3b.

Earlier [1] the advisability was indicated of using equivalent substitution circuits for calculating the frequency error of a photoelectric converter (PC). Let us consider the possibility of representing a converter operating in a specified-current mode or in an intermediate mode (i.e., with \(R_g\)) by a simple equivalent circuit. Let us replace the added resistance and the T-shaped IL by different four-terminal networks; then the converter can be represented as their series connection (Fig. 4a). We reduce this circuit to an equivalent T-shaped one (Fig. 4b). To do this, we find the overall matrix \(A\), equal to the product of the matrices \(A_1\) and \(A_2\).

\[ \left|\begin{matrix} A & B\\ C & D \end{matrix}\right| = \left|\begin{matrix} A_1 & B_1\\ C_1 & D_1 \end{matrix}\right| \cdot \left|\begin{matrix} A_2 & B_2\\ C_2 & D_2 \end{matrix}\right| = \left|\begin{matrix} A_1A_2 + B_1C_2 & A_1B_2 + B_1D_2\\ C_1A_2 + D_1C_2 & C_1B_2 + D_1D_2 \end{matrix}\right|. \tag{2} \]

Then from it we pass to the circuit parameters \(Z_a\), \(Z_b\), \(Z_c\) and determine how they are related to the parameters of the circuit in Fig. 4a.

The matrix \(A\) is written in terms of the circuit parameters in the following form [4]:

\[ \left|\begin{matrix} 1 + \dfrac{Z_a}{Z_c};\; Z_a + Z_b + \dfrac{Z_a Z_b}{Z_c}\\[6pt] 1/Z_c;\; 1 + Z_b/Z_c \end{matrix}\right|. \tag{3} \]

Using (2) and (3), we find

\[ C = C_1A_2 + D_1C_2 = \frac{1}{Z_c} = \left(1+\frac{Z_{a2}}{Z_{c2}}\right)\cdot \frac{1}{Z_{c1}} + \left(1+\frac{Z_{a1}}{Z_{c1}}\right)\cdot \frac{1}{Z_{c2}}, \]

where

\[ Z_{a1}=\frac{1}{2}\left(R_g+j\omega L_g\right)=\frac{1}{2}Z_1; \]

\[ Z_{a2}=\frac{1}{2}\left(R_l+j\omega L_l\right)=\frac{1}{2}Z_2; \]

\[ Z_{c1}=\frac{1}{j\omega C_1},\qquad Z_{c2}=\frac{1}{j\omega C_2}. \]

Fig. 3a. 1—AC source; 2—DC source

Fig. 3b. \(l_f\)—initial length of the transducer; \(U_{fn}\)—readings of the VZ-24 at \(l = l_n\)

Graph labels:

\[ \frac{U_f - U_{fn}}{U_{fn}}\,100\% \]

\[ \frac{l}{l_n} \]

\(l_n\)—initial length of the transducer
\(U_{fn}\)—readings of the VZ-24 at \(l = l_n\)

Fig. 4a

Circuit labels:

\[ Z_{a1},\quad Z_{a1},\quad Z_{a2},\quad Z_{a2} \]

\[ \frac{1}{2}L_g,\quad \frac{1}{2}R_g,\quad C_g,\quad Z_{c1} \]

\[ \frac{1}{2}L_g,\quad \frac{1}{2}R_g \]

\[ \frac{1}{2}L_n,\quad \frac{1}{2}R_n,\quad C_n,\quad Z_{c2} \]

\[ \frac{1}{2}L_n,\quad \frac{1}{2}R_n \]

\(a\)

\(b\)

Fig. 4b

Circuit labels:

\[ Z_a,\quad Z_b,\quad L_g,\quad R_g,\quad L_n,\quad R_n,\quad C_3,\quad Z_c \]

\(C_1, C_2\) are the distributed capacitances of the additional resistance and of the IL relative to the shield, while \(L_g\) and \(L_l\) are, respectively, the total inductances, which also include the lead inductances. Solving the last expression with respect to \(Z_c\) and making the corresponding substitutions, we obtain

\[ Z_c=\frac{2Z_{c1}\cdot Z_{c2}}{2(Z_{c1}+Z_{c2})+Z_1+Z_2}. \]

For real dimensions of the converters, \(C_1\) and \(C_2\) are sufficiently small, and in the frequency range under consideration (up to \(50 \div 100\) MHz) it may be assumed that \(2\cdot (Z_{c2}+Z_{c1}) \gg (Z_2+Z_1)\); then

\[ Z_c \simeq \frac{Z_{c1}\cdot Z_{c2}}{Z_{c1}+Z_{c2}}, \]

i.e., the equivalent capacitance is equal to the parallel connection of the distributed capacitances of \(R_g\) and the IL and is connected to the point of their junction.

From (2) and (3) one may write

\[ A=A_1A_2+B_1C_2 \]

or

\[ 1+\frac{Z_a}{Z_c} = 1+\frac{Z_{a2}}{Z_{c2}} +\frac{Z_{a1}}{Z_{c1}} +\frac{Z_{a1}Z_{a2}}{Z_{c1}\cdot Z_{c2}} +2\frac{Z_{a1}}{Z_{c2}} +\frac{Z_{a1}^{2}}{Z_{c1}\cdot Z_{c2}}. \]

From this equation we find

\[ Z_a= \frac{1}{2}\frac{Z_2\cdot Z_{c1}}{Z_{c1}+Z_{c2}} +\frac{1}{2}\frac{Z_1(Z_{c1}+Z_{c2})}{Z_{c1}+Z_{c2}} +\frac{1}{4}\frac{Z_1(Z_1+Z_2)}{Z_{c1}+Z_{c2}}. \]

Assume that \(Z_{c1}\simeq Z_{c2}\simeq Z_c\); then

\[ Z_a \simeq Z_1\left( \frac{3}{4} +\frac{1}{8}\frac{Z_1}{Z_c} +\frac{1}{8}\frac{Z_2}{Z_c} +\frac{1}{4}\frac{Z_2}{Z_1} \right) \]

and, for \(Z_c \gg Z_1\) and \(Z_2\), we obtain

\[ Z_a \simeq \frac{3}{4}Z_1+\frac{1}{4}Z_2 \]

or \(Z_a \simeq Z_1\), since \(Z_1\) and \(Z_2\) are of comparable magnitude. In a similar way it is also proved that \(Z_b \simeq Z_2\).

Thus, for calculating the comparison error in the high-frequency region, the photoelectric converter may be represented by a T-shaped equivalent circuit (Fig. 4b). In the equivalent circuit obtained, the through distributed capacitance of the additional resistor (Fig. 5) is not taken into account; its influence will be especially noticeable for large values of \(R_g\). As follows from [5], the distributed capacitance may be replaced by an equivalent lumped capacitance of value equal to

\[ C_g \simeq \frac{r\varepsilon}{2\pi}, \]

where \(r\) is the radius of the resistor connected in parallel with \(L_gR_g\). Then the complete equivalent circuit of the PC will have the form shown in Fig. 6. The frequency error of comparison in this case will be equal to

\[ \delta_f = 1- \frac{1}{ \sqrt{(1-\omega^2L_gC_g)^2+\omega^2C_g^2R_g^2} } + \]

\[ + \frac{ \omega^2 C\,(L_gR_l+L_lR_g) }{ (R_g+R_l)\sqrt{(1-\omega^2L_gC_g)^2+\omega^2C_g^2R_g^2} } - \]

\[ - \frac{1}{2} \frac{ \omega^2\left[(L_g+L_l)+C(R_lR_g-\omega^2L_gL_l)\right]^2 }{ \left[(R_g+R_l)-\omega^2C(L_gR_l+L_lR_g)\right] \sqrt{(1-\omega^2L_gC_g)^2+\omega^2C_g^2R_g^2}\cdot |R_g+R_l| }. \tag{4} \]

Since \(L_g C_g = \dfrac{1}{\omega_p^2}\), where \(\omega_p\) is the natural resonant frequency of the added resistance, then, at the frequency of the measured voltage \(\omega \ll \omega_p\) and \(\omega^2 C_g^2 R_g^2 \ll 1\), one may take

\[ \sqrt{(1-\omega^2 L_g C_g)^2+\omega^2 C_g^2 R_g^2} \simeq 1+\frac{1}{2}\omega^2 C_g^2 R_g^2 . \]

In addition, let us note that the terms \(\omega^2 L_g L_l C\) and \(\omega^2 C(L_g R_l+L_l R_g)\) are quantities of the second order of smallness in comparison with the remaining terms, and may be discarded. Taking this into account, (4) is reduced to the simpler form:

Fig. 5

Fig. 6

\[ \delta_f \simeq \frac{\omega^2 C(L_g R_l+L_l R_g)}{R_g+R_l} +\frac{1}{2}\omega^2 C_g^2 R_g^2 -\frac{1}{2}\frac{\omega^2(L+C R_l R_g)^2}{(R_g+R_l)^2}, \tag{5} \]

where

\[ L=L_g+L_l,\qquad C=C_g+C_e . \]

The validity of the calculation relations obtained was checked experimentally by comparison with a standard compensating voltmeter of type V3-24, according to the method described in [1].

The results of studying photoelectric comparators at voltages from 3.8 to 5 V with incandescent lamps of type NSM \(6.3\times20\) are presented in the graphs of Figs. 7 and 8. In the same graphs, the dashed lines show the calculated curves obtained from expression (5). Comparison of the curves obtained by calculation and experimentally shows their good agreement; the discrepancy is no more than 10% in the frequency range up to 100 MHz. This confirms the validity of representing the photoelectric converter by the equivalent circuit (Fig. 6) for the indicated frequency range.

Let us return to expression (5). The presence in it of two terms with different signs indicates the possibility of compensating the frequency error of the comparator; moreover, in the first approximation, with complete compensation, \(\delta_f\) will not depend on frequency*). With incomplete compensation, \(\delta_f\) decreases, and its value remains proportional to the square of the frequency. It is simplest to achieve \(\delta_f=0\) in the PC by changing the capacitance \(C\). In this case two cases are possible:

a) the negative term in (5) is greater than the positive ones.

In this case it is expedient to perform compensation by changing the value of \(C_l\), which, for the known remaining parameters

* This is true for frequencies much lower than the resonant frequency of the converter.

FP \((L_g, L_\ell, R_g, R_\ell, C_e)\) can be calculated from the expression obtained from the condition \(\delta_f = 0\).

\[ C_g = \frac{C_e R_\ell^{\,2} R_g^{\,2} - (L_\ell R_g^{\,2} + L_g R_\ell^{\,2})} {R_g^{\,2} + 2R_g^{\,3}R_\ell} \pm \frac{1}{R_g^{\,2} + 2R_g^{\,3}R_\ell} \times \]

\[ \times \sqrt{ \left[C_e R_\ell^{\,2}R_g^{\,2} - (L_\ell R_g^{\,2} + L_g R_\ell^{\,2})\right]^2 + (R_g^{\,2} + 2R_g^{\,3}R_\ell) \left[ L^2 + C_e^{\,2}R_\ell^{\,2}R_g^{\,2} - 2(L_\ell R_g^{\,2} - L_g R_\ell^{\,2})C_e \right] } \]

The value of the required concentrated capacitance will be determined as

Fig. 7

Visible annotations in the figure: \(\delta\%\); \(\omega\);
1. \(U_k = 3.86\), \(R_g = 150\,\Omega\), \(R_\ell = 150\,\Omega\);
2. \(U_k = 4.56\), \(R_g = 150\,\Omega\), \(R_\ell = 173\,\Omega\);
3. Calculated curve for \(U_k = 3.86\).

Fig. 8

Visible annotations in the figure: \(-\delta\%\); \(\omega\);
1. \(U_k = 56\), \(R_g = 302.4\,\Omega\), \(R_\ell = 146\,\Omega\).

\[ C_{g\,\mathrm{conc}} = C_g - C_\ell', \]

where

\(C_g'\) is the distributed capacitance of the added resistance.

b) the positive terms in (5) are greater than the negative one, i.e.

\[ \delta_f > 0. \]

In this case it is better to carry out the compensation by increasing \(C_{\mathrm{e}}\), the formula for calculating which is given below:

\[ C_{\mathrm{e}}= -\left[ C_g+\left(\frac{L_{\mathrm{l}}}{R_{\mathrm{l}}^2}+\frac{L_g}{R_g^2}\right) \right] \pm \sqrt{ \left[ C_g+\left(\frac{L_{\mathrm{l}}}{R_{\mathrm{l}}^2}+\frac{L_g}{R_g^2}\right) \right]^2 - \left[ \frac{L^2}{R_{\mathrm{l}}^2 R_g^2} - 2C_g\left(\frac{L_{\mathrm{l}}}{R_{\mathrm{l}}^2}+\frac{L_g}{R_g^2}\right) - C_{\mathrm{l}}^2\left(\frac{R_g^2}{R_{\mathrm{l}}^2}+2\frac{R_g}{R_{\mathrm{l}}}\right) \right] }. \tag{7} \]

The lumped capacitance in this case is equal to

\[ C_{\mathrm{e, lump}}=C_{\mathrm{e}}-C_{\mathrm{e}}'. \]

It should be noted that full compensation can be obtained only for one value of \(R_{\mathrm{l}}\), i.e., for one measured voltage. Nevertheless, the introduction of compensating capacitances, even when measuring several voltage values, leads to a reduction in the frequency error. Figure 9 shows the dependences \(\delta_f(R_{\mathrm{l}})\) obtained by calculation. Curves 1, 2, 3 show the behavior of \(\delta_f(R_{\mathrm{l}})\) if compensation is carried out at \(R_{\mathrm{l}}=140,\ 200,\ 260\ \Omega\), respectively. As can be seen from Fig. 9, it is expedient to calculate the compensation for an \(R_{\mathrm{l}}\) chosen in the middle of the working range. For comparison, the same figure gives the dependence \(\delta_f(R_{\mathrm{l}})\) without compensation (curve 4).

The conclusions drawn are rather well confirmed by experiment. In Fig. 7, curve 4 shows the behavior of the frequency error of the converter with an NSM \(6.3 \times 20\) lamp when a compensating capacitance \(C_{g,\mathrm{lump}}\approx 1\) pF, calculated from expression (6), is introduced. The nonmonotonic character of the curve can be explained by the random error of the voltmeter, especially since the scatter lies within the limits of its class. The error increases noticeably only at 200 MHz. Here, evidently, the influence of the approximations adopted in calculating \(\delta_f\) and \(C\) begins to appear.

Fig. 9

Because capacitors produced by industry have a considerable spread of parameters and, in addition, it is difficult to take into account the change in mounting capacitances when setting \(C_{g,\mathrm{lump}}\), etc., we developed a converter design in which provision is made for the possibility of smoothly varying \(C_g\) and \(C\) (Figs. 10a and 10b).

For this purpose the dependence was used of the distributed capacitance of a resistor on the distance between it and a conducting body at zero potential. According to [5], the total capacitance shunting the resistor in this case is equal to

\[ C_g \approx \frac{r\varepsilon_0}{2\pi} \left(1+\frac{2\pi^2 l}{h}\right), \]

where.sulake

\(e\) — length of the resistor,
\(h\) — distance to the conductor.

The results of an experimental study of such a transducer are presented in Fig. 8. Adjustment of the compensating circuit was carried out at two frequencies—100 MHz (curve 3) and 160 MHz (curve 4). The course of the curves indicates that, even with complete compensation at one frequency, there remains a dependence \(\delta_f(\omega)\), which in some cases in the frequency range can even change sign (curve 3), while still remaining considerably smaller than the comparison error without compensation.

Fig. 10a. 1—metal plates,
2—pin for changing \(C_{\mathrm{e}}\)

Fig. 10b

A reduction of the frequency error of the PC can also be achieved by selecting certain design dimensions. Indeed, since \(C_g\), \(C_{\mathrm{e}}\), \(L_g\), and \(L_{\ell}\) depend on the diameter of the external conductor \(D_i\), it is evidently possible to choose its optimum value, at which \(\delta_f \to 0\).

Let us consider the possibility of calculating the internal diameter of the external conductor of the transducer. We take the simplified case in which \(L_g \ll L_{\ell}\), \(C_g \ll C_{\mathrm{e}}\), and their influence may be neglected. Then

\[ \delta_f = -\frac{\omega^2 L_{\ell} C_{\mathrm{e}} R_g}{R_{\ell}+R_g} -\frac{1}{2}\frac{\omega^2\left(L_{\ell}+C_{\mathrm{e}}R_{\ell}R_g\right)^2}{(R_{\ell}+R_g)^2} = \]

\[ = -\frac{\omega^2}{2(R_g+R_{\ell})^2} \left(L_{\ell}^{2}-2L_{\ell}C_{\mathrm{e}}R_g^{2}+C_{\mathrm{e}}^{2}R_{\ell}^{2}R_g^{2}\right). \]

It follows that \(\delta_f=0\) if the expression in parentheses is equal to 0,

\[ L_{\ell}^{2}-2L_{\ell}C_{\mathrm{e}}R_g^{2}+C_{\mathrm{e}}^{2}R_{\ell}^{2}R_g^{2}=0. \]

Denote

\[ \frac{L_{\ell}}{C_{\mathrm{e}}R_{\ell}R_g}=K, \]

then the last expression takes the form

\[ K^2-2\frac{R_g}{R_{\ell}}K+1=0, \]

whence

\[ K=\frac{R_g}{R_{\ell}}\pm \sqrt{\left(\frac{R_g}{R_{\ell}}\right)^2-1}. \]

The obtained relation allows one to conclude that compensation can be obtained only when \(R_g \ge R_{\ell}\).

Using the expression for \(K\) and expressions 6, 7 from [1], we find the optimum diameter of the external conductor

\[ K=\frac{1}{R_{\ell}R_g}\cdot \frac{\mu}{8\pi^2\varepsilon}\cdot \ln\frac{D_i}{d_{\ell}}\cdot \ln\frac{D_i^2}{d_g d_{\ell}}, \]

where \(d_l\) is the diameter of the IL filament,

\(d_g\) is the diameter of the series resistance.

Let us denote \(\ln D_i = A,\ \ln d_l = b,\ \ln d_g = a,\)

\[ K \cdot R_l \cdot R_g \frac{8\pi^2 \varepsilon}{\mu} = \Gamma, \]

then

\[ \ln D_i = A \simeq \frac{a + 3b}{4} \pm \frac{1}{4}\sqrt{(a+3b)^2 - 8(ab + b^2 - \Gamma)}. \]

The solution of this problem in the more general case, taking \(C_g\) and \(L_g\) into account, turns out to be too cumbersome, and therefore we shall confine ourselves to the example considered above, especially since the result is in any case only approximate. It should be noted that obtaining full compensation of the frequency error by selecting the optimum design is very difficult. In addition, when the IL is replaced, even by one of the same type, the compensation is disturbed because of the scatter of parameters, and \(\delta_f\) can then be reduced only by replacing the entire converter structure, which is very inconvenient. In this connection, the approximate diameter of the external conductor should be calculated, while for full compensation of the frequency error the methods described above should be used.

Conclusions

1. When the IL operates in the specified-current mode and the intermediate error of comparison substantially depends on the place where the IL is connected: with an inductive character of the series resistance, the minimum error is attained when the IL is brought as close as possible to the short-circuited end of the converter; with a capacitive character of the series resistance, the IL should be connected closer to the input of the converter.

2. It is possible to reduce the frequency error by changing the distance between the IL and the short-circuited end of the converter.

3. For calculating the frequency error, the PC may be represented in the form of a T-shaped equivalent circuit. The validity of such a substitution is well confirmed by experiment.

4. It is possible to reduce the frequency error by selecting the optimum dimensions of the converter structure or by introducing special compensating circuits.

5. Compensation of the frequency error may be carried out at one frequency. In measurements at other frequencies, \(\delta_f\) will not appear if full compensation has been performed; otherwise, the quadratic dependence on frequency of the uncompensated part of the error remains.

6. Full compensation is retained only for one value of the measured voltage, at which the adjustment was performed. For other values \(\delta_f\) will be present, while remaining considerably smaller than the error without a compensating circuit.

LITERATURE

1. Yu. M. Fomichev, M. S. Roitman. Error of photoelectric converters at high frequencies. Tomsk, Tomsk State University Press, Izv. TPI, 1970, vol. 231.

2. F. L. Hermach, E. S. Williams. Thermal voltage Converters for Accurate voltage Measurements to 30 Mgs. Communication and Electronics, July, 1960.

3. R. F. Aknaev, T. B. Rozhdestvenskaya. New apparatus for measuring the rms value of voltage in a wide frequency range. Izmeritel’naya tekhnika, 1970, No. 5.

4. N. V. Zernov, V. G. Karpov. Theory of Radio-Engineering Circuits. Moscow—Leningrad, “Energiya,” 1965, p. 264.

5. M. S. Mikitinskii. Allowance for the distributed capacitance of nonwire resistances. Radiotekhnika, 1963, vol. 18, No. 1.