MEASUREMENT OF PARASITIC CAPACITANCES IN VACUUM-TUBE CIRCUITS

D. I. Sviryakin

(Presented by Professor-Doctor V. I. Gorbunov)

In the experimental verification of analytical methods for calculating various radio circuits, it becomes necessary to determine, with sufficient accuracy, the magnitudes of all parasitic capacitances that affect the operation of the circuit. Reference values of the interelectrode capacitances of tubes cannot always satisfy the experimenter, since the capacitances of each particular tube specimen, not only in the heated but also in the cold state, differ from those given in the reference book; moreover, in the circuit there are added to them capacitances existing between the corresponding lugs of the tube socket, as well as between the wires and components connected to these lugs. Therefore the total interelectrode capacitances acting in the circuit turn out to be greater than the capacitances of the tube itself.

The task of measuring the wiring capacitance and each of the interelectrode capacitances is complicated by their mutual influence on one another. That is, when attempting to measure one of them, one measures a total capacitance composed of the measured capacitance connected in parallel and the capacitances of chains made up of other parasitic capacitances connected in series. This means that, for correct measurement of the required capacitance, it is necessary to neutralize or exclude from the measurement circuit all the others. A study of the capacitance-measurement methods described in the literature [1, 2, 3] showed that the stated problem can be solved by a differential bridge and by the measurement procedure set forth below.

The E8-1 instrument (“PIMEL”), intended for measuring the interelectrode capacitances of tubes not included in a circuit, is built according to a transformer differential AC bridge circuit with two strongly coupled inductive arms. The supply-voltage frequency of the measuring bridge is 465 kHz. Therefore, when measuring capacitances shunted by resistors whose values, at the measurement frequency, are comparable with the values of the capacitive reactances, it is necessary to disconnect one of the terminals of each of these resistors, trying not to disturb the geometry of the circuit mounting. This operation may, to one degree or another, distort the measurement results, but, as experience shows, the error increases by no more than 2–5%.

For convenience of the subsequent exposition, Fig. 1 gives a simplified circuit of the differential bridge of the E8-1 instrument. The circuit consists—

consists of the differential transformer \(Tr_1\) and the autotransformer \(Tr_2\), the halves of whose windings form the two arms of the differential circuit. These arms are made of mutually coupled inductors with a coupling coefficient close to unity. The strong coupling between the winding halves ensures constancy of the transformation ratio and symmetry of the voltages even with asymmetrical loads on each arm of the differential circuit. In addition,

Fig. 1. Simplified circuit of a differential measuring bridge

such a circuit provides high stability of the arm parameters under the influence of all possible destabilizing factors. The primary winding of transformer \(Tr_1\) is connected to a high-frequency generator (465 kHz). The reference three-terminal differential variable capacitor and the capacitance being measured form the two other arms of the differential circuit. The circuit provides for compensation of the active losses of the measured capacitance by means of the fixed nonreactive resistor \(R_2\) and the potentiometer \(R_1\). By turning the potentiometer slider, the active attenuation in the arm with the reference capacitor is varied, and in this way the losses of the measured capacitor are balanced. The parasitic capacitances between the potentiometer terminals are connected in parallel with part of the winding of the autotransformer \(Tr_2\) and do not affect the measurements. Capacitor \(C_2\) blocks the path of the dc component of the current when capacitances are measured in circuits to which a dc voltage is applied. The error due to this capacitor is no more than 0.5–1.0%, since its capacitance is sufficiently large (2200 pF).

The measured capacitance \(C_x\) is connected to the terminals of the instrument marked in Fig. 1 by the numerals 1 and 2. All capacitances connected between each of these terminals and terminal 3 are excluded from the measurements. This is precisely the advantage of the differential bridge in comparison with others. Thus, the problem of measuring parasitic capacitances in circuits requires combining all interfering capacitances into one or two groups and connecting these groups between terminals 1–3 and 2–3. The measured capacitance must then be connected to terminals 1–2.

Below, using pentode resistive amplifiers as an example, methods are shown for rearranging circuits that make it possible to measure any of the interelectrode capacitances, as well as the wiring capacitance \(C_m\) and the total overall capacitance \(C_0\). In the case of triode circuits, the measurements will present no difficulties, since eliminating the corresponding circuits only simplifies the circuit.

Figure 2 shows a circuit for measuring the interelectrode capacitance of a pentode, grid–cathode \(C_{\mathrm{gk}}\). Here, in order to exclude all other capacitances from the measurements, the anode and the screen grid of the tube are shorted to a common conductor, and one of the filament leads is also connected to the same common conductor. To eliminate, in this case, the short-circuiting of the power-supply source through the resistors \(R_{\mathrm{f}}, R_{\mathrm{a}}, R_{\mathrm{s}}\) to the common conductor, it is necessary to disconnect the resistors \(R_{\mathrm{f}}\) and \(R_{\mathrm{s}}\), respectively, from the capacitors \(C_{\mathrm{f}}\) and \(C_{\mathrm{s}}\), without disturbing their position relative to the holder of the other parts of the circuit. The elements of the cathode circuit \(C_{\mathrm{k}}\), \(R\) must be disconnected from the common conductor, likewise without changing their position in the wiring. Disconnecting these elements will eliminate overloading of one arm of the measuring bridge (terminals 2–3), which would make balancing the bridge difficult or make the measurements altogether impossible. To eliminate overloading of the bridge arm connected between terminals 1–3, it is necessary to disconnect capacitor \(C_{\mathrm{p1}}\) from the anode of the preceding stage or from the signal generator \(U_{\mathrm{g}}\). If resistor \(R_{\mathrm{c}}\) has a value of less than \(100\ \mathrm{k\Omega}\), it too must be disconnected from the common conductor, without changing its position relative to the tube socket and the other parts.

Fig. 2. Circuit for measuring interelectrode capacitance.

To avoid repetition below when describing the subsequent measurement circuits, we shall agree that, in all the circuits, the points of disconnection are marked by crosses, and the position of the disconnected parts in the wiring is not changed; the connection points of the “PIMEL” instrument are marked by small circles with the numbers 1, 2, and 3, which correspond to the terminals of the instrument shown in Fig. 1. The parasitic capacitance measured in the circuit under consideration, and the conductors connecting the corresponding circuits in order to exclude all the other capacitances from the measurements, are shown by solid heavy lines. The parasitic capacitances excluded (but not shunted) from the measurements, owing to the newly introduced connecting conductors, are shown by dashed lines. Capacitances that have been shunted by these conductors are not shown in the circuits. Common to all the circuits, along with the already mentioned designations of the elements of the cathode and anode circuits and of the screen-grid circuit, are the following designations: \(C_{\mathrm{gk}}\) is the control grid–cathode capacitance, \(C_{\mathrm{ga}}\) is the control grid–anode capacitance, \(C_{\mathrm{ak}}\) is the anode–cathode capacitance, \(C_{\mathrm{kh}}\) is the cathode–heater capacitance, \(C_{\mathrm{m}}\) is the wiring capacitance of the corresponding part of the circuit, \(C_{\mathrm{p}}\) is the coupling capacitor, and \(R_{\mathrm{c}}\) is the leakage resistor. Additional numerical subscripts introduced into the designations of elements indicate that the given element belongs to one or another stage or section of the circuit.

Figure 3 gives a circuit for measuring the parasitic output capacitance \(C_2\) of a stage, which is composed of the anode–cathode and anode–screen-grid capacitances \((C_{\mathrm{as}})\), i.e., \(C_2 = C_{\mathrm{ak}} + C_{\mathrm{as}}\). Capacitance \(C_1\) in this circuit combines the capacitances control grid–cathode, ca-

then—the heater and the mounting capacitance of the screen grid (including the capacitance between the control and screen grids). If the resistance of the load connected to the output of this stage is not less than \(100\ \text{k}\Omega\), and the capacitance of this load is comparable with the mounting capacitance \(C_{\mathrm{m}}\), then the load need not be disconnected when measurements are being carried out. Disconnection of the circuit \(R_{\mathrm{k}} C_{\mathrm{k}}\) is performed for the same reasons as in the circuit shown in Fig. 2.

Fig. 3. Circuit for measuring the output capacitance

Figure 4 shows the circuit for measuring the feedthrough capacitance \(C_{\mathrm{ca}}\) of a tube connected in an amplifier stage. The capacitance denoted in this circuit as \(C_1\) is the parallel combination of the grid—cathode capacitance of the tube and the mounting capacitance at the stage input, i.e. \(C_1 = C_{\mathrm{ck}} + C_{\mathrm{m1}}\). The capacitance \(C_2\) includes the anode—cathode and anode—screen-grid capacitances, i.e. \(C_2 = C_{\mathrm{ak}} + C_{\mathrm{ae}}\). Disconnecting the resistor \(R_{\mathrm{c}}\) from the common wire and disconnecting the load at the output of the stage are carried out here under the same conditions as in the case of measurements according to the circuits of Figs. 2 and 3.

Fig. 4. Circuit for measuring the feedthrough capacitance

With the aid of the circuit in Fig. 5, the parasitic capacitance of the circuit wiring connected between the anode of the first tube and the control grid of the second is measured with respect to the common wire (and the chassis, if

they are electrically connected). The output capacitance of the first stage here is the sum of the parasitic capacitances, as in the case of the circuit in Fig. 3, but is denoted by \(C_1 = C_{\mathrm{ak}1} + C_{\mathrm{az}1}\). The subscript 1 here denotes affiliation with the first stage. Disconnection of the load of the second stage

Fig. 5. Circuit for measuring the parasitic capacitance of the wiring

and of the leakage resistor \(R_{\mathrm{c}1}\) of the first stage in this case is subject to the same conditions as in the circuits of Figs. 2 and 3.

The circuit of Fig. 6 is intended for measuring the total summed cathode–heater capacitance \(C_{\mathrm{kp}}\) [[unclear: adjoining text]]; they are not indicated, since they are included for the anode load resistor \(R_{\mathrm{a}1}\) of the first stage, \(C_o = C_2 + C_{\mathrm{m}} + C_{\mathrm{sk}2}\), where \(C_2 = C_{\mathrm{ak}1} + C_{\mathrm{az}1}\) is the output capacitance of the first stage, \(C_{\mathrm{m}}\), as in the circuit of Fig. 5, is the wiring capacitance, and \(C_{\mathrm{sk}2}\) is the grid–cathode capacitance of the tube of the second stage.

In this circuit \(C_1 = C_{\mathrm{sk}1} + C_{\mathrm{az}1}\) and \(C_3 = C_{\mathrm{sa}2} + C_{\mathrm{sz}2}\).

The general considerations listed above remain valid for this circuit as well. It should only be noted that here, as in Fig. 4, the cathode–heater capacitances \(C_{\mathrm{kp}}\) are not indicated, since they are connected in parallel with the capacitors \(C_{\mathrm{k}}\) shunting the cathode resistors and, naturally, cannot appreciably change the values of the capacitors \(C_{\mathrm{k}}\).

The capacitance measurements in each of the circuits described above are carried out as follows. First, in accordance with the corresponding circuit, the necessary switching is performed, after first disconnecting the supply voltages. Then, to the points indicated in the circuits by the numbers 1 and 2, a previously calibrated E8-1 bridge (“PIMEL”) is connected by copper busbars or by single-core wires 1.5–2.0 mm in diameter. The busbars or wires are shaped so that, without elastic deformation, they fit exactly the points of the circuit to which they are to be connected. The terminal of the instrument designated by the number 3 must be connected to the points in the circuits marked by the same number. These points may be connected to the terminal by a flexible multicore wire, which, if possible, should not pass between the first two, since with three wires it is more difficult than with two to keep their shape and the distance between them unchanged. The instrument is connected to the circuit by “crocodile” clips soldered to the busbars, or by soldering. The latter method, despite its greater complexity, is more reliable and disturbs the geometry of the wiring less.

After the bridge has been connected, the supply voltages may be applied to the circuit; this will make it possible to measure the interelectrode capacitances with the filaments switched on. Having carried out, in accordance with the operating instruc-

…of the E8-1 instrument, the required capacitance value having been measured, the circuit must be carefully disconnected from the conductors connecting it to the bridge and removed. At the same time, the distance between these conductors and their position relative to one another must remain unchanged, in order to keep the parasitic capacitance between them unchanged. Having measured with the bridge—

Fig. 6. Circuit for measuring the total parasitic capacitance

—this capacitance, its value must be subtracted from the previously obtained result. The result of the subtraction will give the value of that parasitic capacitance for the measurement of which all these operations were performed.

The measurement error under the most unfavorable conditions, but with observance of all the requirements listed above, does not exceed 10%. A check measurement may be the measurement of the capacitance \(C_0\) according to the circuit of Fig. 6. The measured value of this capacitance must be equal to the sum of the capacitance values obtained as a result of measurements according to the circuits of Figs. 2, 3, 4, and 5.

REFERENCES

1. G. A. Remez. A Course in Basic Radio-Engineering Measurements. Svyaz’ Publishing House, Moscow, 1966.
2. E. G. Momot. Radio-Engineering Measurements. Gosenergoizdat, Moscow–Leningrad, 1957.
3. N. M. Meerson. Radio-Measurement Engineering. Energiya Publishing House, Moscow–Leningrad, 1967.