Electrical diagram of a device for measuring the capacitance of capacitors. Homemade measuring instruments. Microfaradmeters with serial and parallel measurement schemes

Almost two years ago I bought a digital capacitance meter, I took, one might say, the first thing that came across. I was so tired of the inability of the Mastech MY62 multimeter to measure the capacitance of capacitors more than 20 microfarads, and it did not measure correctly less than 100 picofarads. I liked two factors in the SM-7115A:

1. Measures the entire required range
2. Compactness and convenience

Paid 750 rubles. He sincerely believed that he was not worth the money, and the price was "inflated" due to the complete absence of competitive products. The country of origin is, of course, China. He was afraid that he would "fake" Furthermore I was sure of it - but in vain.

The capacitive meter and wires to it were packed in polyethylene, each in its own sheath and enclosed in a box of thick cardboard, free space filled with foam. Also included in the box were instructions for English language. dimensions device 135 x 72 x 36 mm, weight 180 grams. The body color is black, the front panel with a lilac tint. It has a liquid crystal display, nine measurement ranges, two power off positions, a zero adjustment knob, 15 centimeter, different color(red - black) wires, with which the measured capacitor is connected to the device, end with crocodile clips, and the sockets on the body of the device for connecting them are marked with a color designation of the corresponding polarity, it is additionally possible to measure without them (which increases accuracy) , for which there are two oblong sockets, which are signed with the symbol of the measured capacitor. A 9 volt battery is used, there is a function for automatically indicating its discharge. Three-digit liquid crystal indicator +1 decimal place, the measurement range declared by the manufacturer is from 0.1 pF to 20,000 μF, with the possibility of adjustment on the measurement range from 0 to 200 pF, to set zero, within +/- 20 pF, one measurement time 2-3 seconds.

Table of permissible errors in measurements, individually by ranges. Provided by the manufacturer.

There is an integrated stand on the back half of the case. It makes it possible to more compactly place the meter in the workplace and changes in better side overview of the liquid crystal display.

The battery compartment is made completely autonomously, to change the battery, it is enough to move its cover to the side. Convenience from the category of inconspicuous, when it is.

In order to remove the back cover of the case, it is enough to unscrew one self-tapping screw. The heaviest PCB component is the 500mA fuse.

The operation of the measuring device is based on the method of double integration. It is assembled on logical counters HEF4518BT - 2 pcs, key HEF4066BT, decimal counter with decoder HCF4017 and smd transistors: J6 - 4 pcs, M6 - 2 pcs.

Having unscrewed six more screws, you can see the other side of the printed circuit board. The variable resistor with which the setting is made to "0" is so that it can be easily replaced if necessary. On the left are the pins for connecting the measured capacitor, those above are for direct connection (without wires).

The device is set to the zero reference point not immediately, but the set reading holds. With the wires disconnected, this is much easier to do.

To visually demonstrate the difference in measurement accuracy with different ways measurements (with and without wires) took small capacitors with factory markings - 8.2 pF

Video review of the device

Without wires With wires
#1 8 pF 7.3 pF
#2 7.6pF 8.3pF
#3 8.1pF 9.3pF

Everything is clear, unambiguously without wires, measurements will be more accurate, although the discrepancy is practically within 1 pF. I also repeatedly measured the capacitors on the boards - the measurement readings of the serviceable ones are quite adequate according to the denomination indicated on them. If not to be a very big nitpick, then it is quite possible to say that the quality factor of the measurement of the device is quite high.

Disadvantages of the device

• setting to zero is not done immediately,
• the petals of the contacts, for measuring without wires, have no elasticity, after unclenching they do not return to their original position,
• The meter is not equipped with a calibration container.

conclusions

In general, I am satisfied with the device. It measures well, it is compact (it easily fits in a pocket), so on the radio market I take not what they give, but what I need. I plan, as there will be time, to finalize: to replace the potentiometer and contacts for direct measurement. His scheme, or something similar, can be searched in the section. He told “everything as it is”, and you already decide for yourself whether it is worth replenishing home laboratory such a device. Author - Babay.

The main parameters characterizing capacitors are their electric capacitance and loss angle.

The permissible error in measuring the capacitances of capacitors depends on the field of application of the latter. The capacitance of the capacitors that make up the oscillatory systems must be determined especially carefully, with an error of at least 1%. When choosing blocking, separating, coupling, etc. capacitors, a significant (up to 20-50%) variation in capacitances is usually allowed and they can be measured using the simplest methods.

Rice. 1. Equivalent circuits (a, b) and vector diagram (c) of a circuit with a capacitor

In each capacitor included in electrical circuit, there are energy losses that occur mainly in the dielectric material, as well as due to the imperfection of the insulation between the terminals. Taking into account the losses, the equivalent circuit of a capacitor can be represented in two versions: either in the form of a capacitance C connected in series with the loss resistance R p (Fig. 1, a), or in the form of the same capacitance C, shunted by a leakage resistance R y (Fig. 1 , b). When moving from one equivalent circuit to another to recalculate the value active resistance use the formula

R y \u003d 1 / ((2 * π * f * C) 2 * R p) ,

where f is the frequency of the current in the capacitor circuit.

From vector diagram in fig. 1, c, which is valid for both variants of equivalent circuits, it follows that in a circuit with a capacitor, due to the presence of losses, the phase shift φ between current I and voltage U is always less than 90 °. Losses in a capacitor are usually characterized by a loss angle δ = 90° - &phi, determined in accordance with the notation in Fig. 1 from the formula

tg δ \u003d U p / U c \u003d Iy / Ic \u003d 2 * π * f * C * R p \u003d 1 / (2 * π * f * C * R y).

Losses in the capacitor are sometimes expressed by the power factor cos φ or the leakage current Iy, determined at standard conditions. For most capacitors, losses are very small (tg δ< 0,001), поэтому можно считать

tg δ ≈ δ ≈ sin δ \u003d sin (90 ° - φ) \u003d cos φ.

The greatest losses occur in electrolytic and paper capacitors, the use of which is mainly limited to the low-frequency region.

With some measurement methods, losses in a capacitor are determined simultaneously with the measurement of its capacitance. It should be borne in mind that with increasing frequency, the losses increase markedly (which corresponds to an increase in the value of R p and a decrease in R y), while the capacitance C is practically independent of frequency. At very high frequencies, a noticeable increase in the effective (measured by instruments) capacitance of capacitors is possible due to the influence of the inductance of the plates and lead wires.

Capacitor parameters (С, R n , R y , δ) depend on external conditions its work - temperature, humidity, atmospheric pressure, as well as the voltage applied to it. Therefore, in critical cases, testing of capacitors is carried out not only at their operating frequencies, but also under conditions close to operational ones.

The simplest checks of capacitors can be made without special measuring instruments. With an ohmmeter or probe, it is easy to detect short circuit or a breakdown between the plates of the capacitor (it should only be taken into account that the breakdown sometimes manifests itself only with a significant voltage on the capacitor, close to its operating voltage). Checking for an open circuit of non-electrolytic capacitors with a capacity of 0.01 microfarads and above is most easily done by including a capacitor in the circuit alternating current, for example, lighting or broadcasting, in series with any load - an incandescent lamp, a loudspeaker, etc. Normal or slightly weakened lamp glow or the sound of a radio transmission will indicate that there is no break.

A capacitor, the leakage resistance of which is high, is able to hold for a long time without a noticeable decrease in the charge received by it; this allows simple means evaluate the quality of capacitors with a capacity of more than 0.01 uF. When an ohmmeter is connected to such a capacitor, the arrow of the meter of the latter deviates somewhat due to the charge current, and then (with a large leakage resistance) returns to its original position or close to it. Subsequent short-term connections to the ohmmeter capacitor, repeated at intervals of several seconds, should not cause the meter to deviate. With a low leakage resistance, a noticeable deviation of the needle will be observed each time an ohmmeter is connected. To test for leakage of capacitors larger than 100 pF, headphones can be used connected in series with a low-voltage battery. With a low leakage resistance, each connection of the indicator to the capacitor causes a click in the phones, while with a good capacitor, a click is heard only at the first connection. Measuring the leakage resistance value (per DC) can be produced by inductor or electronic megohmmeters.

Electrolytic capacitors must be connected to the test instrument with respect to the polarity of the power supply. When measuring the leakage resistance of such capacitors, it is recommended that the reading be made 10 minutes after they are turned on under voltage, when the charging process can be considered completed.

To measure the parameters of capacitors, the methods of a voltmeter - ammeter, direct measurement using microfaradmeters, comparison (substitution), bridge and resonant methods are used.

The voltage applied to the capacitor during any test shall not exceed the allowable operating voltage. If during the test the capacitor is charged to a significant voltage, it is necessary to discharge it at the end of the test (for example, using a button connected in parallel with the capacitor).

Capacitance measurement by voltmeter - ammeter method

Rice. 2. Schemes for measuring capacitances using the voltmeter-ammeter method

The measurement scheme is presented in two versions in Fig. 2. The capacitor Cx under test is connected to an alternating current circuit of a known frequency F, and a rheostat (or potentiometer) R sets the value of current I or voltage U required by the test conditions or convenient for reading. According to the readings of alternating current devices V and mA you can calculate the impedance of a capacitor

Z \u003d (R 2 + X 2) 0.5 \u003d U / I, (1)

where R and X = 1/(2*π*F*C x) are its active and reactive components, respectively.

If the losses are small, i.e. R<< X, то измеряемая ёмкость определяется формулой

C x \u003d I / (2 * π * F * U). (2)

The scheme in fig. 2, a, gives fairly accurate results when measuring large capacitances, the resistance of which X is much less than the input resistance of the voltmeter V. The circuit in fig. 2, b, is used to measure smaller capacitances, the resistance of which is tens or more times higher than the resistance of a milliammeter mA. Suppose that it is required to measure capacitances in the range of 0.1-1 μF at a frequency of 50 Hz with a 3 mA AC milliammeter. Since the resistance of these capacitances X = 3200 ... 32000 Ohm is many times greater than any possible resistance of a milliammeter, the measurement should be carried out according to the circuit in fig. 2, b, at supply voltage U ≥ I*X = 0.003*3200 ≈ 10 V.

The scheme in fig. 2, but can also be used to measure the capacitance of electrolytic capacitors. If the supply voltage does not exceed 1-2 V, then the measurement can be carried out when the switch is installed IN to position 1. At high alternating voltages, capacitors may be damaged due to electrolyte decomposition. This danger is eliminated if switch B is set to position 2. In this case, a direct current source is switched on in series with an alternating current source of frequency F, the voltage at the terminals of which U 0 must exceed the amplitude of the alternating voltage. Then a pulsating voltage will act in the circuit, which is safe for the capacitor, provided that the polarity of its inclusion in the circuit is correct. A ripple voltage can also be obtained by connecting a diode in series in the measuring circuit. In all cases, the voltmeter V and milliammeter mA should measure only the variable components of voltage and current, for which they are performed with a closed input circuit.

Microfaradmeters with serial and parallel measurement schemes

Devices in which the assessment of the measured capacitances is carried out directly on the scale of the pointer meter are called microfaradmeters. The operation of these devices can be based on the use of the dependence of current or voltage in a circuit supplied by an alternating current source, on the value of the measured capacitance of the capacitor included in it. The circuits of such devices are in many ways similar to the circuits of ohmmeters and megohmmeters.

Microfaradmeters can have a serial or parallel measurement circuit. The series circuit (Fig. 3) is used to measure capacitances of average values ​​(from about 100 pF to 10 μF). The voltage U of frequency F is supplied from the source to the circuit in which the reference capacitance C o, the capacitor under test C x and the micro- (or milli) AC ammeter are connected in series mA. Before starting measurements, with a short circuit of the input terminals (which is equivalent to C x \u003d ∞), a rheostat R is installed in the microammeter circuit mA total deflection current I p; this is ensured by choosing the capacity of the reference capacitor

C 0 ≥ I p (2*π*F*U). (3)

When the capacitor C x is connected, the current through the microammeter will decrease to a certain value I x, the smaller, the smaller the capacitance C x, which allows the meter to be equipped with a scale with marks for the values ​​of the measured capacitances. The calibration characteristic of the device does not depend on the frequency and shape of the supply voltage curve and is approximately determined by the formula

I x / I p ≈ C x / (C o + C x), (4)

identical to the formula that determines the calibration characteristic of parallel circuits of ohmmeters. The measurement error also changes similarly: the smallest in the middle of the scale, it increases towards its edges. The middle of the scale corresponds to the capacity C x ≈ C o, and the measurement range is limited to 0.1 C o and 10 C o. The required supply voltage is determined from the condition

U ≥ I p / (2*π*F*C o).

For example, at I p = 1 mA, F = 50 Hz and C o = 20000 pF, the power supply must provide voltage U ≥ 160 V, but if the source oscillation frequency F = 1000 Hz, then the required supply voltage is reduced to 8-10 V.

To measure capacitances in a wide range, the microfaradmeter must have several measurement limits, which it is advisable to set by the average values ​​of the C o scale with a transition factor N that is a multiple of 10.

Rice. 3. Series circuit of a microfaradmeter with a current meter

The most convenient power source for the microfaradmeter is an alternating current network with a frequency of 50 Hz, which makes it possible to obtain any required voltage using a small-sized transformer. A high value of the latter is necessary only on the limits with the smallest capacitances C o. If we limit the maximum supply voltage to 200 V, then in the presence of a rectifier microammeter mA per 100 μA, according to (3), the capacitance of CO is 1600 pF. It is permissible to turn on high-voltage power only after the capacitor C o is discharged and the capacitor under test is connected to the circuit. To close the input terminals in order to set the meter pointer to the “∞” mark, it is advisable to use a button. Capacitors C o and C x must be designed for an operating voltage not less than the test voltage. To prevent damage to the meter in the event of a breakdown of the capacitor C o, it is advisable to make the latter of two capacitors connected in series, each with a capacity of 2C o. It is also possible to include a limiting resistor in the power circuit with a resistance 5-10 times less than the capacitance of the capacitor C o.

To expand the measurement range towards large values ​​of C o, at the beginning, the supply voltage is usually reduced by N times (until it reaches a few volts), using taps from the windings of a power transformer or using a resistive voltage divider. The transition to limits with an even greater value of C o may be accompanied by a decrease in the sensitivity of the indicator by shunting it, similar to how it is done in multi-limit ohmmeters. The upper limit of the measured capacitances usually does not exceed 1-10 μF, since with a capacitor resistance C o comparable to the internal resistance of the indicator and the power circuit, the measurement error greatly increases.

When expanding the measurement range towards small values ​​of C o, in order to obtain acceptable values ​​of the supply voltage U, the circuit has to be powered from an internal or external generator - a high-frequency voltage source F of thousands of hertz. At the same time, it is necessary to take measures to eliminate the influence of the circuit's own capacitances and installation.

Diagram of the microfaradmeter according to fig. 3 will also operate when replacing the reference capacitor C o with the reference resistor R o. In this case, the selected average value C on the capacitance measurement scale will be achieved with a resistance

R o ≈ (4 * U 2 / I 2 p - 1 / (2 * π * F * C o) 2) 0.5

Such a device can be simultaneously used as an ohmmeter with a serial circuit for an approximate measurement (at a frequency F) of active resistances, provided that the reading is performed on a special scale similar to the capacitance scale, but reversed.

Rice. 4. Sequential circuit of a multi-limit microfaradmeter with a voltage meter

In the presence of an electronic AC voltmeter with a large input resistance Rv, the circuit shown in fig. 4. Alternating voltage U, stabilized by the chain R1, D1, D2 and approximately equal to the measurement limit U p of the voltmeter V, when the input terminals are closed, it acts on the voltmeter. By adjusting the sensitivity of the latter, the arrow of its meter is deflected to the end of the scale. When the tested capacitor C x is included in the circuit, a voltage divider R o, C x is formed, from which voltage U x is applied to the voltmeter, the smaller the capacitance C x is. The selected average value C o of the capacitance scale will be achieved with resistance R o ≈ 1 / (11 * F * C o). By switching resistors R about different ratings, the measurement limits of capacitances are changed. The minimum possible value of capacitance C o is limited by the maximum allowable resistance value R o ≈ 0.1 R o. For example, with R o \u003d 1 MΩ and a frequency F \u003d 50 Hz, we get the capacitance C o ≈ 1 / (11 * F * R o) \u003d 1820 pF.

The microfaradmeter in the considered mode of its operation has the extreme marks of the capacitance scale "0" and "∞". However, if you use a sensitive millivoltmeter in the device with a measurement limit U p<< U, допускающий кратковременную случайную перегрузку до напряжения, равного U, то верхние пределы измерения прибора могут быть ограничены выбранными значениями ёмкостей С п, которым должны соответствовать сопротивления

R o ≈ U p / (U * 2 * π * F * C p) ;

at the same time, the working section of the scale is significantly expanded. In this case, with an acceptable resistance R o \u003d 1 MΩ, a frequency F \u003d 50 Hz and a voltage ratio U p / U \u003d 1/30, we get С p ≈ 100 pF, which allows measuring capacitances from 10 pF or more. If the order of the measured capacitance C x is unknown, then the switch IN you should initially set the measurement limit for the largest capacities, at which the possible overload of the voltmeter is limited due to the increase in the voltage drop across the resistor R1.

In a microfaradmeter with limited measurement limits, it is necessary to calibrate the device before starting measurements. In the diagram in fig. 4 for this purpose is the chain R2, C1. When the Kn button is pressed from the capacitor C1, a voltage is applied to the input of the voltmeter, at which the arrow of its meter should deviate to the end of the scale (or to a certain mark on the scale), which is achieved by the sensitivity regulator. Usually they take R2 equal to the resistance R about one of the measurement limits, and C 1 equal to the capacitance C p of the same limit.

On fig. 5a shows one of the variants of the parallel circuit of the microfaradmeter. With free input terminals (which is equivalent to capacitance C x \u003d 0), by adjusting the sensitivity of the voltmeter V, the arrow of its meter is deflected to the end of the scale. The inclusion of a capacitor C x in the circuit leads to the fact that the voltage on the voltmeter, initially equal to U p, decreases to the value U x, the smaller, the larger the capacitance C x. The calibration characteristic of the microfaradmeter is determined by the formula

U x /U p ≈ C o /(C o + C x), (5)

a similar formula that determines the calibration characteristic of sequential ohmmeter circuits.

The input resistance of the voltmeter R in and the supply current frequency F limit the choice of the reference capacitance of the capacitor C o, which determines the average value of the scale, by the condition

C about ≥ 1.5 / (F * R in) .

For example, at Rv = 1 MΩ and F = 50 Hz, we get C o ≥ 30,000 pF, i.e., the device is suitable for measuring only relatively large capacities (not electrolytic!) With a high-frequency power source, it is possible to reduce the allowable values ​​of C o to hundreds picofarad, however, the measurement error can be large if you do not take into account the input capacitance of the voltmeter.

Rice. 5. Parallel circuits of microfaradmeters

To measure the capacitance of electrolytic capacitors, the circuit in fig. 5 B. Due to the inclusion of the diode D, a pulsating voltage U o acts on the voltage divider R1, R2. At C x \u003d 0, from the resistor R2 to the voltmeter V (it can be relatively low-resistance, for example, rectifier), a total deviation voltage U p is applied. Turning on the capacitor C x leads to a decrease in the voltage on the voltmeter in accordance with formula (5). With the selected average value of the capacitance scale C o and frequency F = 50 Hz, the required values ​​​​of the resistance of the voltage divider are determined by the formulas:

R1 \u003d U o / (U p * 180 * C o); R2 \u003d R1 * U p (U o -U p).

Changing the measurement limits is carried out by using several voltage dividers with the same division factor U o /U a, but different values ​​of the resistances R1 and R2. The AC voltmeter V must have a closed input circuit, otherwise it must be energized through a large electrolytic capacitor.

All the considered circuits of microfaradmeters make it possible to measure the capacitances of capacitors with an error of 5-10%, and sometimes more. It is not always possible to perform their scale based on the calculation of the calibration characteristic due to the influence of various factors that are difficult to take into account, for example, the internal resistances of the power source and measuring instruments, the non-linearity of the voltage scale of the voltmeter, etc. Therefore, when adjusting and calibrating microfaradmeters, it is necessary to use capacity magazines or sets of capacitors with capacity tolerances not more than 5%.

Example 1. Calculate the serial circuit of the microfaradmeter according to fig. 3 to the measurement limit from C n \u003d 200 pF to C m \u003d 20000 pF, provided that the supply voltage should not exceed 10 V. In the device, use a 1 mA milliammeter as a meter.

Instruction. The middle of the scale corresponds to the capacity C o ≈ (C n C m) 0.5.

Answer: C o \u003d 2000 pF, F ≥ 8 kHz. When choosing F = 10 kHz U ≥ 8V, R = 3...5 kOhm

Answer: C o \u003d 3 uF, R1 \u003d 37 kOhm, R2 \u003d 2 kOhm; C "o \u003d 30 uF, R" 1 \u003d 3.7 kOhm, R "2 ≈ 200 Ohm.

Microfaradmeters with a uniform scale

A microfaradmeter with a uniform scale can be made according to a scheme similar to the schemes of capacitive frequency meters, differing in principle from the latter only in that the object of measurement is not the frequency, but the capacitance. The operation of such devices is based on measuring the average value of the charge or discharge current of the tested capacitor, recharged by a voltage of known frequency.

On fig. 6, a, shows a diagram of the measuring unit of a microfaradmeter powered by a rectangular pulse voltage u. During the action of the pulse, the capacitor C x is charged through the diode D to a maximum voltage U m. In the interval between pulses, the capacitor is discharged through the meter (magnetoelectric microammeter) And to the initial voltage U n. In steady state, with the input pulse repetition rate f and their amplitude U p = U m - U n, the average value of the current flowing through the meter I x = C x U p f. With fixed values ​​of U p and f, the meter can be equipped with a uniform scale with a reading in C x values ​​in accordance with the formula

C x \u003d I x / (U p f).

Limit value of measured capacitances

C p \u003d I and / (U p f),

where I and - the total deviation current of the meter. To smooth out ripples and eliminate fluctuations in the meter needle, a capacitor C is used, the resistance of which at a frequency f should be significantly less than the resistance R and the meter.

The results will not change if the meter is included in the charging current circuit in series with diode D2 (Fig. 6, b); then the discharge current of the capacitor C x will be closed through the diode D1. When measuring small capacities, a two-half-wave meter switching circuit is sometimes used (Fig. 6, c). In this case, both charging and discharging currents flow through the meter, which makes it possible to obtain the required measurement limit at a voltage U p or a frequency f that is half that in circuits with a half-wave meter.

Rice. 6. Schemes of measuring blocks of microfaradmeters with a uniform scale

The measurement limits of the device are set by the values ​​C p and to ensure them, when switching the limits, they change the pulse repetition rate of the power source, determined by the formula

f = I and (U p C p) . (6)

Before starting measurements at each limit, the microfaradmeter should be calibrated, for which a capacitor with a capacity of C o \u003d C p is connected to it by pressing the Kn button (Fig. 6, a); at the same time, the deviation of the meter arrow to the end of the scale is achieved by smoothly adjusting the frequency f, the amplitude of the pulses U p or the sensitivity of the meter (for example, using a shunt rheostat R w). Since the scale of the device is uniform, the measurement error of capacitances is mainly determined by the selection error of the reference capacitance C o, the deviation of which from the required nominal value (C p) should not exceed 1 ... 5%.

To obtain the correct measurement results, it is necessary that in one period of the input voltage and the capacitor C x has time to fully charge and discharge (within the voltages U m - U n). This is most easily achieved with a rectangular shape of the input pulses and an appropriate choice of their repetition frequency f.

As is known, in a circuit consisting of elements R and C, the duration of the charge (discharge) of the capacitor C to the value of the constant voltage applied to this circuit is determined by the time constant τ = RC and practically does not exceed 5τ. In order for the charge (discharge) to end during the half-cycle T/2 of the voltage of frequency f, the condition must be satisfied

5RC = 5 τ<= T/2 = 1/(2*f),

which is satisfied at the frequency

f<= 1/(10*RС). (7)

Taking the maximum possible resistance of the charge and discharge circuits R = 10 kΩ (taking into account the output resistance Rout of the pulse generator), we obtain a practical formula for choosing the pulse repetition frequency (in kilohertz):

f ≤ 10 4 / C p (8)

(where C p - in picofarads). In the last condition, the equal sign is often taken. Then the upper measurement limits C p - 100, 1000, 10,000 pF and 0.1 μF will correspond respectively to the frequencies f = 100, 10, 1 and 0.1 kHz.

Condition (8) and formula (6) determine the required pulse amplitude (in volts):

U p ≥ 0.1*I and

(where I and are in microamps). For example, when working with a meter having a total deviation current I and = 100 μA, an amplitude U p ≥ 10 V is required.

The resistance of the resistor R d (Fig. 6, a) is taken such that the resistance of the meter circuit R d + R and significantly exceeds (at least tens of times) the direct resistance of the diode D; at the same time, it should not increase the total resistance of the discharge circuit beyond the allowable value (10 kΩ). If both conditions cannot be simultaneously satisfied, then the resistor R d is replaced by a diode that passes the discharge current; in this case, the meter turns on according to the circuit in Fig. 6b. When calculating the device, the nature of the output resistance Rout of the pulse generator is also taken into account, which, depending on the generator circuit, can be constant, adjustable, or even nonlinear (large during the pulse and small in the interval between pulses).

In addition to a uniform capacitance scale, microfaradmeters can have an uneven scale with a reading range from 0 to ∞, similar to the scales of parallel ohmmeter circuits. The nature of the scale (uniform - P, uneven - H) in the diagram in fig. 6, a, is determined by the setting of the switch B1. In the position of the last "H", the tested capacitor C x is connected in series with the reference capacitor C o, the capacitance of which sets the measurement limit of the device and approximately corresponds to the middle of its non-linear scale.

A uniform capacitance scale can also be obtained by some other methods. So, if a differentiating circuit R, C x is connected to the output of the multivibrator, then the average voltage of pulses of the same polarity taken from the resistor R turns out to be proportional to the capacitance C x. To work in such a device, a sensitive DC millivoltmeter is required. The measurement limits can be set by the resistances of the resistor R. At a pulse repetition rate f = 100 kHz, the upper limits of capacitance measurement C n = 10 and 100 pF were obtained.

Example 3. Make an approximate calculation of the measuring unit of a microfaradmeter with a uniform scale (Fig. 6, a) for measuring capacitances with upper limits of 300 and 3000 pF, 0.03 and 0.3 μF, if the device meter has data: I and = 50 μA , R and = 2600 Ohm.

Answer: C o \u003d 300 and 3000 pF, 0.03 and 0.3 microfarads; f = 30 and 3 kHz, 300 and 30 Hz; R d \u003d 1.5 kOhm; R w \u003d 10 kOhm; C = 5..10 uF; U p \u003d 5 V; R out ≤ 6 kOhm.

Capacitance measurement by comparison (substitution) method

This method is based on comparing the effect exerted by the measured capacitance C x and the known capacitance C o on the mode of the measuring circuit.

The simplest measurement scheme, in which the capacitances C x and C o are compared by the value of their resistance to alternating current, is shown in fig. 7. When the capacitor C x is turned on, the potentiometer R sets a current in the circuit that is convenient for reading or monitoring with an alternating current milliammeter mA or other low resistance indicator. Then, instead of the capacitor C x, a store of capacitances or an exemplary (reference) capacitor of variable capacity is connected to the circuit and by changing its capacitance C o the previous indicator reading is achieved. This will take place at C o = C x. The measurement error depends on the sensitivity of the indicator and the error in reading the capacitance C o; it can be obtained equal to about 1% or less.

Rice. 7. Capacitance measurement scheme

When measuring capacitances above 5000 pF by the comparison method, the measurement circuit can be powered from an alternating current network with a frequency of 50 Hz. To measure smaller capacitances, an oscillator operating at higher frequencies is needed. In all cases, to ensure the safety of the indicator, a limiting capacitor (C1) or resistor should be included in the circuit.

The comparison method in various versions is widely used in bridge and resonant capacitance meters. It can also be implemented in microfaradmeters, discussed in the previous paragraphs, with a significant reduction in the measurement error.

AC measuring bridges

To measure the parameters of capacitors and inductors, balanced AC bridges are widely used.

In the general case, the arms of the AC measuring bridge (Fig. 8) have complex resistances Z1, Z2, Z3 and Z4, one of which, for example Z4, is the object of measurement. The bridge is powered from an alternating current source of frequency F, the voltage of which is supplied directly or through a transformer Tr to one of the diagonals of the bridge. The other diagonal turns on the AC zero indicator IN.

Rice. 8. AC bridge circuit

Just like in DC bridges, the measurement process is reduced to balancing the AC bridge, which is characterized by the absence of a potential difference between the vertices A And b; this requires that the voltage drops in the arms Z1 and Z4 (as well as in the arms Z2 and Z3) be equal in amplitude and coincide in phase. Equilibrium is achieved when two conditions are met:
1) the equality of the products of the modules of the impedances of the opposite arms, i.e.

Z 4 Z 2 = Z 1 Z 3 ; (9)

2) the equality of the sums of the phase angles of the same arms, i.e.

φ4 + φ2 = φ1 + φ3 . (10)

If the bridge arm has active R and reactive (capacitive or inductive) X resistances acting in series, then the arm impedance modulus

Z \u003d (R 2 -X 2) 0.5, (11)

and its phase angle φ is determined from the formula

tg φ = X/R . (12)

For purely active arms (X = 0) the phase angle φ = 0; for purely capacitive and inductive arms (R = 0) respectively φ = -90° and φ = +90°. If the shoulder resistance has a mixed (complex) character, then the phase angle |φ|< 90°.

If the resistances R and X are presented in parallel, then the arm impedance modulus

Z \u003d 1 / (1 / R 2 + 1 / X 2) 0.5, (13)

and the phase angle φ is found from the formula

tg φ = R/X . (14)

In this case, the angle φ = 0 in the absence of reactance (X = ∞) and φ = +-90° in the absence of active resistance (R = ∞).

For the simultaneous fulfillment of both equilibrium conditions, it is necessary to adjust two parameters of the known bridge arms; in this case, it becomes possible to determine two parameters of the studied arm, for example, the active and reactive components of its impedance.

Condition (9) can always be fulfilled by adjusting the elements of the bridge arms. The second condition (10) is feasible only with a certain layout of the bridge circuit, for example, if all four arms consist of the same elements - resistors, capacitors or inductors. Usually, in order to simplify the circuit, the two arms of the AC bridge are made up of active resistance elements - resistors. If these arms are adjacent (Fig. 9), then the other two arms must have reactances of the same nature, that is, both must contain either capacitors or inductors. If the active resistance arms are opposite, then the other two arms must have reactances of a different nature: one is capacitive, and the other is inductive, having phase angles of different signs, the sum of which can be made equal to zero.

In measuring bridges of alternating current, the use of inductors is avoided (unless, of course, the latter are objects of measurement), since they have a noticeable active resistance and are susceptible to magnetic fields; moreover, with a steel core, the inductance of the coil is not stable. Variable resistors and capacitors, as well as resistance and capacitance stores, are used as adjustable elements in bridges.

In the simplest bridges powered by audio frequency sources, headphones are often used as zero indicators. The bridge is balanced by the minimum audibility of the fundamental frequency tone, which reduces the measurement error due to the action of harmonics, and allows you to reduce the requirements for the power generator.

In industrial measuring bridges, rectifier or electronic millivoltmeters, as well as oscilloscope indicators on small cathode ray tubes, are used as zero indicators; the latter, unlike other indicators, have phase sensitivity, which makes it possible to determine the direction in which the bridge should be balanced.

The advantages of balanced AC bridges are a small measurement error, which does not exceed 1% in the best samples, wide measurement limits, and the possibility of universal application for measuring various electrical quantities. Their main disadvantage is the complexity and duration of the balancing process. In the latter respect, unbalanced and automatic AC bridges have certain advantages.

In unbalanced AC bridges, the amplitude and phase of the output voltage at the terminals of the indicator diagonal depend both on the module and on the composition of the measurement object Zx. With a relatively small deviation from the equilibrium state, the active and reactive components of the output voltage turn out to be approximately proportional to the increments of the analogous components of the complex resistance Zx relative to those values ​​at which the bridge is balanced By means of two phase-sensitive systems, it is possible to separate the components of the output voltage, shifted in phase by 90 °, which are then separated measured by two indicators; the report on the scales of the latter is made respectively in the values ​​of the active and reactive components of the resistance Zx.

In automatic AC bridges, the components of the output voltage selected by phase-sensitive systems drive two electric motors, which, through drives, act on the adjustment elements of the bridge circuit until the equilibrium state is reached.

Bridge method for measuring capacitor parameters

Bridges used to measure the parameters of capacitors are divided into magazine and reochord (linear). The simplest (single-limit) magazine bridge, suitable for measuring capacitances of tens and hundreds of picofarads, can be composed of four capacitors: a measured capacitor with a capacitance scale (in the adjacent arm) and two constants with the same capacitance (hundreds of picofarads). When used as an indicator of headphones, the bridge can be powered by a radio network. Wide-range magazine bridges are more complicated than reochord bridges, but they provide less measurement error and can have uniform reading scales. The range of capacitances measured by the bridge method lies approximately in the range from 10 pF to 10 ... 30 μF.

On fig. 9, a is a diagram of a multi-limit magazine bridge. It is balanced with a variable capacitor C1 and a variable resistor R1. Applying the equilibrium condition (9) to this scheme, we obtain

R2*(R x 2 + 1/(2*π*F*C x) 2) 0.5 = R3*(R1 2 +1/(2*π*F*C 1) 2) 0.5

Given that φ 2 = φ 3 = 0, the second equilibrium condition (10) can be written as the equality φ x = φ 1 or tg φ x = tg φ 1 or, according to formula (12),

1/(2*π*F*C x *R x) = 1/(2*π*F*C 1 *R 1).

Solving the above equations together, we find:

C x \u003d C1 (R2 / R3) ; (15)

Rx = R1(R3/R2) . (16)

With a fixed ratio of the resistances of the shoulders R2 / R3, the capacitor C1 and the resistor R1 can be equipped with scales with a reading, respectively, in the values ​​of capacitances C x and loss resistances R x. The expansion of the measurement range is achieved by using a group of switchable resistors R3 (or R2) of various ratings, usually differing by 10 times. The bridge balances quickly because the adjustments made by capacitor C1 and resistor R1 are mutually independent. If the bridge is intended to measure capacitances less than 0.01 uF, for which losses at low frequencies are very small, then resistor R1 may be absent.

Rice. 9 Diagrams of magazine bridges for measuring the parameters of capacitors

In order to simplify the design in some measuring bridges, the capacitor C1 is taken with a constant capacity, and two variable resistors are used as adjustable elements, for example R1 and R2 (Fig. 9, b). From formulas (15) and (16) it follows that both adjustments of such a bridge turn out to be interconnected, therefore its balancing, controlled by the readings of the rectifier indicator, should be carried out by successively approaching the minimum by alternately changing the resistances R1 and R2. The capacitance values ​​C x are on the scale of the resistor R2, taking into account the multiplier determined by the setting of the switch IN. Since a direct assessment of the loss resistance R x is impossible, the reading on the scale of the resistor R1 is usually performed in the values ​​of the loss tangent:

tg δ = 2*πF*C x *R x = 2*π*F*C 1 *R 1 ,

which at a fixed frequency F is uniquely determined by the value of the resistance R1. It is easy to verify the validity of the last formula if we multiply the left and right sides of equalities (15) and (16), respectively.

Simple capacitance meters are made according to the reochord bridge scheme, which usually provides for the possibility of measuring both resistances, and sometimes inductances. A diagram of a universal reochord bridge is given in the article Measuring the parameters of inductors in fig. 5.

Example 4 9, b, for measuring capacitances at three limits with upper values ​​of 10,000 pF, 0.1 and 1 μF, as well as the loss tangent from 0 to 0.01, if the capacitance C1 = 0.01 μF, and the impedance R2 is 10 kOhm Supply voltage 10 V, frequency 50 Hz. Meter AND has parameters: I and = 100 μA, R and = 900 Ohm.

The calculation results are shown in the diagram.

Resonant capacitance meters

In addition to measuring the frequency of electrical oscillations, resonant methods are widely used to measure small capacitances and inductances, quality factors, natural or resonant tuning frequencies, and other parameters of radio components and oscillatory systems.

The resonant capacitance measurement circuit (Fig. 10) usually includes a high-frequency generator, with the circuit of which LC is weakly connected inductively (or through a capacitance) by a measuring circuit consisting of a reference inductor L o and a capacitor under test C x. By changing the capacitance of the capacitor C, the generator is tuned into resonance with the natural frequency f o of the measuring circuit according to the extreme readings of the resonance indicator, for example, an electronic voltmeter V. With a known generator tuning frequency f o, the measured capacitance is determined by the formula

C x \u003d 1 / ((2 * π * f o) 2 * L o) ≈ 0.0253 / (f o 2 L o) (17)

With a fixed value of L o, the capacitor C can be equipped with a scale with a reading in capacitance values ​​C x.

The limits of capacitance measurements are determined by the value of the inductance L o and the frequency range of the generator. For example, with L o = 100 μH and a generator range of 160-3500 kHz, the device will measure capacitances from tens of picofarads to hundredths of microfarads. To expand the limits of measuring capacitances with a limited frequency range of the generator, several replaceable coils L with different inductances are used, and the tested capacitors are also included in the measuring circuit in series with capacitors of a known capacitance. Capacitances of more than 0.01-0.05 μF are usually not measured by the resonance method, since at low frequencies the resonant curves of the oscillatory circuits become dull, which makes it difficult to fix the resonance.

As resonance indicators, sensitive high-frequency devices are used that respond to current or voltage acting in the measuring circuit, for example, electronic voltmeters with a pointer or electronic light indicator, electron beam oscilloscopes, thermoelectric devices, etc. The resonance indicator should not introduce noticeable attenuation into the measuring circuit.

Rice. 10. Scheme for measuring capacitances by the resonance method

The upper limit of the capacitances measured by this method is equal to the difference between the maximum C m and the initial C n capacitances of the capacitor C o. Capacitors whose capacitance exceeds the value C m - C n can be connected to the circuit in series with a constant capacitor of known capacity Cx. In this case, the order of measurements remains the same, but the measured capacitance is calculated by the formula

C x \u003d C1 (C o1 - C o2) / (C 1 - C o1 + C o2).

For example, at C 1 \u003d 600 pF, C o1 \u003d 500 pF and C o2 \u003d 100 pF, we get C x \u003d 1200 pF. Using several replaceable capacitors C1 of various ratings, you can get a number of measurement limits. If we set the upper limit of the measured capacities C p, then the required capacity C x is determined by the formula:

C 1 \u003d C p (C m -C n) / (C p -C m + C n).

For example, with C p \u003d 2000 pF, C m \u003d 500 pF and Cn \u003d 20 pF, the capacitor should have a capacitance C1 \u003d 630 pF.

Various variants of resonance methods are implemented in special measuring instruments or by means of small-sized attachments to standard radio equipment with frequency scales (the latter include high-frequency measuring generators, radio receivers, etc.).

Rice. 11. Diagram of a resonant capacitance meter using the absorption phenomenon

On fig. 11 shows a diagram of a resonant capacitance meter based on the use of the absorption (absorption) phenomenon. The device contains a low-power generator according to the capacitive three-point scheme, with the oscillatory circuit of which the measuring circuit L2, C6, C7 is inductively connected. The connection between the circuits is made relatively strong (eg, by using a common ferrite core for coils L1 and L2) in order to ensure a noticeable influence of the measuring circuit on the oscillator mode. The resonance indicator is a DC microammeter mA, included in the base circuit of the transistor T. When the measuring circuit is tuned to resonance with the generator frequency, the energy absorbed by the circuit turns out to be the largest. This causes a sharp decrease in the constant component of the base current, measured by a microammeter mA, which provides a clear fixation of the resonance state.

To reduce the measurement error of small capacitances, two variable capacitors (C6 and C7 in Fig. 11) with maximum capacitances, for example, 500 and 50 pF, can be included in the measuring circuit. Before measurements, both capacitors are set to maximum capacity and, using the tuning core of one of the coils, the resonant tuning of the generator and the measuring circuit is achieved. Then, by attaching a capacitor C x to the circuit, depending on the estimated capacitance of the latter, one of the capacitors C6 or C7 restores resonance. Reading on the scales of capacitors C6 and C7 is desirable to produce directly in the values ​​​​of capacitances C x.

Figure 12. Scheme for measuring capacitances by the resonant method using a radio receiver

The considered version of the resonance method can be implemented using the simplest attachment to a radio receiver with an internal magnetic antenna. The prefix (Fig. 12) is a measuring circuit L, C o, the natural frequency of which, at the maximum value of capacitance C o, must be within any frequency subrange of the receiver. The receiver is tuned to the frequency of one of the well-received transmitting radio stations of this subband, and then the coil L is placed near the receiver, parallel to its magnetic antenna. At the highest capacitance With the tuning core of the coil L, the circuit is tuned to resonance with the tuning frequency of the receiver, which is detected by the weakening of the audibility of the radio station's audio signals, and then the capacitance C x is measured by the substitution method.

High accuracy of fixing the resonance state is achieved with the heterodyne method (zero beat method). In a heterodyne capacitance meter, there are two identical high-frequency local oscillators, the oscillations of which are mixed in a detector stage loaded on telephones. At the maximum capacitance of the main variable loop capacitors, both local oscillators are tuned to the same frequency, which is controlled by zero beats. Then, in parallel with one of these capacitors, a capacitor C x is included, the capacitance of which is determined by the substitution method.

If both local oscillators are made completely identical, then the device can be successfully used to equalize the capacitances of double and triple blocks of variable capacitors. To do this, one section of the tested block of capacitors is simultaneously connected to the circuits of both local oscillators and zero beats are achieved with their maximum capacitance. If both sections are the same, then with a conjugate decrease in their capacitances, zero beats should be preserved.

An unambiguous relationship between the capacitance of the oscillatory circuit of the generator and the frequency of the excited oscillations allows you to create a capacitance meter, consisting of a generator, the circuit of which includes capacitors C x, and a frequency meter that has a scale with a direct reading of C x values.

In all variants of the application of the resonance method, the preliminary adjustment of the measuring circuit should be carried out with the conductors connected to it to communicate with the object of measurement, the length of which should be as short as possible.