Today, there are many devices on the market that measure capacitance and inductance, but they cost several times more than a Chinese multimeter. Anyone who needs to measure capacitance or inductance every day will certainly buy one for themselves, but what to do if such a need arises extremely rarely? In this case, you can use the method described below.
It is known that if a rectangular pulse is applied to the integrating RC chain, the shape of the pulse will change and will be the same as in the picture.
The time during which the voltage on the capacitor reaches 63% of the supplied voltage is called tau. The formula by which tau is calculated is shown in the figure.
In this case, they say that the integrating chain has smoothed out the fronts of the rectangular pulse.
It is also known that if a rectangular pulse is applied to a parallel LC circuit, damped oscillations will appear in the circuit, the frequency of which is equal to the resonant frequency of the circuit. The resonant frequency of the circuit is found using Thomson's formula, from which the inductance can be expressed.
The circuit is connected through a small capacitor, the smaller the better, which limits the current entering the circuit. Let's look at how a small capacitor limits current.
In order for the capacitor to charge to the rated voltage, a certain charge must be transferred to it. The smaller the capacitance of the capacitor, the less charge it needs for the voltage on the plates to reach the pulse voltage. When we apply a pulse, a small capacitor charges very quickly and the voltage on the capacitor plates becomes equal to the pulse voltage. Since the voltage of the capacitor and the pulse are equal, there is no potential difference, hence no current flows. Moreover, the current may stop flowing through the capacitor after some time from the start of the pulse, and for the remainder of the pulse time, no energy will be supplied to the circuit.
To carry out the experiment, we need a rectangular pulse generator with a frequency of 5-6KHz.
You can assemble it according to the diagram in the figure below or use a signal generator, I did it both ways.
Now, remembering how the integrating RC chain and parallel LC circuit behave when a rectangular pulse is applied, let’s assemble the simple circuit shown in the picture.
First, let's measure the capacitance of the capacitor; its connection location in the diagram is indicated as C?. I didn't have a 1K resistor on hand, so I used a 100 Ohm and instead of a 10pF capacitor I used a 22pF capacitor. In principle, you can choose any resistor value, but not lower than 50 Ohm, otherwise the generator voltage will drop significantly.
In this experiment, I will use a signal generator whose output impedance is 50 Ohm. Let's turn on the generator and set the amplitude to 4V; if you assemble the generator according to the circuit, you can adjust the amplitude by changing the supply voltage.
Let's connect the oscilloscope probes in parallel with the capacitor. The following picture should appear on the oscilloscope.
Let's increase it a little.
Let's measure the time during which the voltage on the capacitor reaches 63% of the pulse voltage or 2.52V.
It is equal to 14.8uS. Since the generator resistance is connected in series with our chain, it must be taken into account; as a result, the active resistance is equal to 150 Ohm. Let's divide the tau value (14.8 uS) by the resistance (150 Ohm) and find the capacitance, it is equal to 98.7 nF. On the capacitor it is written that the capacitance is 100nF.
Now let's measure the inductance. In the diagram, the connection location of the inductor is marked L?. We connect the coil, turn on the generator and connect the oscilloscope probe parallel to the circuit. On the oscilloscope we will see the following picture.
We increase the scan.
We see that the oscillation period is 260KHz.
The probe capacitance is 100pF and in this case it must be taken into account because it is 10% of the circuit capacitance. The total capacitance of the circuit is 1.1nF. Now let’s substitute the capacitance of the capacitor (1.1nF) and the oscillation frequency (260KHz) into the form to find the inductance. For such calculations I use the Coil32 program.
The result is 340.6uH; judging by the marking, the inductance is 347uH and this is an excellent result. This method allows you to measure inductance with an error of up to 10%.
Now we know how to measure the capacitance of a capacitor and the inductance of a coil using an oscilloscope.
Devices for direct assessment and comparison
Measuring instruments for directly assessing the value of the measured capacitance include microfaradmeters, the action of which is based on the dependence of the current or voltage in the alternating current circuit on the value included in it. The capacitance value is determined using the dial meter scale.
More widely used for measuring inductances AC balanced bridges, allowing to obtain a small measurement error (up to 1%). The bridge is powered by generators operating at a fixed frequency of 400-1000 Hz. Rectifier or electronic millivoltmeters, as well as oscilloscope indicators, are used as indicators.
The measurement is made by balancing the bridge as a result of alternate adjustment of its two arms. The readings are taken from the limbs of the handles of those arms with which the bridge is balanced.
As an example, let's consider the measuring bridges that are the basis of the EZ-3 inductance meter (Fig. 1) and the E8-3 capacitance meter (Fig. 2).
Rice. 1. Bridge circuit for measuring inductance
Rice. 2. Bridge circuit for measuring capacitance with small (a) and large (b) losses
When the bridge is balanced (Fig. 1), the inductance of the coil and its quality factor are determined by the formulas Lx = R1R2C2; Qx = wR1C1.
When balancing bridges (Fig. 2), the measured capacitance and loss resistance are determined using the formulas
Measuring capacitance and inductance using the ammeter-voltmeter method
To measure small capacitances (no more than 0.01 - 0.05 μF) and high-frequency inductors in the range of their operating frequencies, resonant methods are widely used. The resonant circuit usually includes a high-frequency generator, inductively or through a capacitance connected to the measuring LC circuit. Sensitive high-frequency devices that respond to current or voltage are used as resonance indicators.
The ammeter-voltmeter method measures relatively large capacitances and inductances when the measuring circuit is powered from a low frequency source of 50 - 1000 Hz.
For measurements, you can use the diagrams in Fig. 3.
Figure 3. Circuits for measuring large (a) and small (b) alternating current resistances
According to instrument readings, the total resistance
Where
from these expressions one can determine
When active losses in a capacitor or inductor can be neglected, use the circuit in Fig. 4. In this case
Rice. 4. Schemes for measuring large (a) and small (b) resistances using the ammeter-voltmeter method
Measuring the mutual inductance of two coils
The simplest and most accessible way for radio amateurs to measure the inductance of a low-frequency coil (low-frequency inductor, steel-core transformer winding, etc.) is as follows:
1) assemble the circuit shown in Fig. ; as a device that measures voltage across a variable resistor R and coil L x use a tester or a separate AC voltmeter; the maximum resistance value of the resistor with a dissipation power of 0.25-1-0.5 W is chosen within the range of 100-30000 Ohms (depending on the expected value).
2.32. Measuring the inductances of low-frequency coils
2) installed using an autotransformer AT voltage is at 10 V and notice the reading U 1 voltmeter, that is, the voltage drop across the coil being tested;
3) move the switch slider from position 1-3 to position 1-2 , thus connecting a voltmeter in parallel with the resistor, and selecting such a resistance value R = R 2, at which the voltage drop across the resistor is also equal to U 1.
4) calculate the inductance of the coil using the formula:
L" x = 0.00318 √ RR 2 Gn, (32)
Where R 1 And R 2- resistor resistance (Ohm) when the switch slider is in positions 1-3 and 1-2.
In the absence of a variable resistor, the inductance of the coil is measured using a fixed resistor. The measurement scheme and process remain the same, but the formula for calculating L x- supplemented by a multiplier U 1/U 2, that is, takes the form:
L"" x = 0.00318 R(U 1 /U 2) Gn, (33)
Where R- resistor resistance, Ohm,
U 1 And U 2- voltmeter readings in positions 1-3 and 1-2 of the switch slider.
In most cases, the inductive resistance of the windings is much higher than their active resistance, so the above formulas give fairly accurate inductance values.
However, if the number of coil turns is small and the resistance to direct (or alternating) current is high (several tens or hundreds of Ohms), then L" x And L"" x calculated using other, more accurate formulas, namely:
Where R- resistor resistance when the switch slider is in position 1-2; U- voltage across series-connected R And Lx; U 2- the voltage across the resistor is equal to the voltage U 1 on reel L x;
L x " = 0.00318 R 0 / tan α,
Where R- active resistance of the winding;
α - the angle formed by side BC of triangle ABC () and the perpendicular lowered from point B to the continuation of side LS.
Rice. 2.40. Stress triangle defining angle α
Tangent of the angle α they find it like this. Lay down on an arbitrary straight line MN() line segment AC, proportional to voltage U 2 on a resistor R. Then draw from the points A And WITH, both from centers, with radii proportional to stress U power supply and voltage U 1 on the winding, two arcs. Connect the dot IN intersection of these arcs with a point WITH and drop from the point IN perpendicular BD directly MN. Finally, lengthen the height BD triangle ABC up to 100 mm (segment DK) and pass through the point TO direct KP, parallel to the side Sun triangle ABC. If we take the segment DK per unit, then cut off on the straight line MN line segment P.D. and will be numerically equal to the tangent of the angle α .
In cases where the coil's DC resistance exceeds its inductive reactance, measure Lx carried out at a different, higher frequency (for example, 400 or 800 Hz). The voltage waveform at the output of the voltage source of this increased (audio) frequency must be sinusoidal.
Rice. 2.41. On the issue of finding the tangent of an angle α
When moving to a frequency not equal to 50 Hz, instead of the coefficient, enter into formulas (32) ~ (35) 0,00318 factor 1/2π f power supply circuit, where f- frequency of the circuit power supply.
The vast majority of amateur inductance meters on controllers measure the frequency of a generator operating at frequencies of about 100 kHz, and although they supposedly have a resolution of 0.01 μH, in fact, with inductances of 0.5 and below they are a good random number generator, not a device. The developer of radio frequency devices has three ways:
- break off
- buy an industrial impedance meter and fast for a while
- do something more high-frequency and broadband.
The presence of many online calculators radically simplifies the task; you can get by with just one generator connected to a frequency meter, without losing much in convenience, but gaining in functionality.
The attachment can measure inductance from 0.05 μH. Output voltage is about 0.5V. The self-inductance of the terminals is 0.04 μH. Output frequency range: xs...77 MHz.
The wideband generator is made according to the well-known two-point circuit and is little sensitive to the quality factor of the frequency-setting circuit. 
To measure the smallest inductances, the capacitance chosen was 82pf; together with the input capacitance, the calculated value (for the calculator) is about 100pf (round numbers are more convenient), and the max. generation frequency is about 80 MHz. From the circuit, voltage is supplied to the repeater vt2 and from it to the emitter vt1, thus implementing a PIC. The sometimes used direct connection of the gate to the circuit leads to unstable operation of the generator at frequencies of 20-30 MHz, therefore an isolation capacitor c1 is used. The field-effect transistor must have an initial drain current of at least 5 mA, otherwise the transistor must be slightly opened with a resistance of several hundred kOhms from positive to the gate. It is better to use a transistor with a high transconductance, this will increase the output voltage taken from the source. Although the generator itself is practically insensitive to the types of transistors.
Online calculators are used for calculations
The most convenient
most inconvenient
glamorous but with character
The setting capacity in the device can be anything, even Chinese clay. It is better to have reference coils and insert the measured capacitance into the calculator, although in reality this is not necessary.
The foil on the reverse side is used as a screen.
The leads to the coil are made in the form of flexible flat braided leads 2 cm long. with crocodiles.
http://edisk.ukr.net/get/377203737/%D0%B8%D0%BD%D0%B4.lay6
Features of use.
For power supply, it is better to provide a corresponding terminal on the frequency meter.
The leads to the coil should be as straight as possible if ultra-low inductances are measured. From the result you need to subtract the self-inductance of the terminals 0.04 μH. The minimum measurable inductance is approximately the same.
To measure inductances up to 100 μH, a standard capacitance is suitable; above it, it is better to use additional capacitances from 1N, otherwise there will be an error from the interturn capacitance of the coil.
To measure the interturn capacitance, you need to measure the true value of inductance with C 10-100n, then the frequency with the standard capacitance (100pf) is measured, entered into the calculator, then the total capacitance is calculated, from which you need to subtract 100pf.
Example. axial inductor 3.8 mH, with standard capacitance frequency 228 kHz, total capacitance 128 pF, turn-to-turn 28.
Capacitances in circuits are calculated in the same way.
To measure chokes on low-frequency LV magnetic circuits, they must have a sufficiently large number of turns, for example, on 2000NN rings at least 20, otherwise the frequency may be higher than the operating frequency for them (up to 400 kHz), and the generation will be disrupted at best, and pulsed at worst, as in a blocking generator, with a frequency of kilohertz. For low-turn ones, additional capacity is needed.
The main parameter characterizing loop coils, chokes, and transformer windings is inductance L. In high-frequency circuits, coils with inductance from hundredths of a microhenry to tens of millihenries are used; coils used in low-frequency circuits have inductances of up to hundreds and thousands of henries. It is advisable to measure the inductance of high-frequency coils that are part of oscillatory systems with an error of no more than 5%; in most other cases, a measurement error of up to 10-20% is acceptable.
Rice. 1. Equivalent circuits of an inductor.
Each coil, in addition to inductance L, is also characterized by its own (interturn) capacitance C L and active loss resistance R L distributed along its length. Conventionally, it is believed that L, C L and R L are concentrated and form a closed oscillatory circuit (Fig. 1, a) with its own resonant frequency
f L = 1/(LC L) 0.5
Due to the influence of capacitance C L, when measured at high frequency f, it is not the true inductance L that is determined, but the effective, or dynamic, value of the inductance
L d = L/(1-(2*π*f) 2 *LC L) = L/(1-f 2 / f L 2)
which may differ markedly from the inductance L measured at low frequencies.
As the frequency increases, losses in inductors increase due to the surface effect, energy radiation, bias currents in the winding insulation and frame, and eddy currents in the core. Therefore, the effective active resistance R d of the coil can significantly exceed its resistance R L measured with an ohmmeter or a DC bridge. The quality factor of the coil also depends on the frequency f:
Q L = 2*π*f*L d /R d.
In Fig. 1, b, shows the equivalent circuit of the inductor taking into account its operating parameters. Since the values of all parameters depend on frequency, it is advisable to test coils, especially high-frequency ones, at the oscillation frequency of the power source corresponding to their operating mode. When determining test results, the subscript “d” is usually omitted.
To measure the parameters of inductors, the main methods used are voltmeter - ammeter, bridge and resonant. Before measurements, the inductor must be checked for open circuits and short-circuited turns. An open circuit is easily detected using any ohmmeter or probe, while identifying short circuits requires a special test.
For simple tests of inductors, cathode ray oscilloscopes are sometimes used.
Indication of short-circuited turns
Checking for the absence of a short circuit is most often carried out by placing the test coil near another coil that is part of the oscillatory circuit of the autogenerator, the presence of oscillations in which and their level are controlled using telephones, a dial, electronic light or other indicator. A coil with short-circuited turns will introduce active losses and reactance into the circuit connected to it, reducing the quality factor and effective inductance of the circuit; As a result, the oscillations of the self-oscillator will weaken or even fail.
Rice. 2. Scheme of a resonant capacitance meter using the absorption phenomenon.
A sensitive device of this type can be, for example, a generator made according to the circuit in Fig. 2. A coil with short-circuited turns, brought close to the loop coil L1, will cause a noticeable increase in the readings of the microammeter μA.
The test circuit can be a serial circuit tuned to the frequency of the power source (see “Radio”, 72-5-54); the voltage on the elements of this circuit, monitored by some indicator, under the influence of short-circuited turns of the coil being tested will decrease due to detuning and increasing losses. It is also possible to use a balanced AC bridge, one of the arms of which in this case should be a communication coil (instead of the L x coil); short-circuited turns of the tested coils will cause an imbalance in the bridge.
The sensitivity of the test device depends on the degree of connection between the coil of the measuring circuit and the coil being tested; in order to increase it, it is advisable to place both coils on a common core, which in this case is open.
In the absence of special instruments, a radio receiver can be used to test high-frequency coils. The latter is tuned to some well-audible station, after which the coil being tested is placed near one of its operating loop coils, for example a magnetic antenna (preferably on the same axis with it). If there are short-circuited turns, the volume will noticeably decrease. A decrease in volume can also occur if the receiver tuning frequency is close to the natural frequency of the coil being tested. Therefore, to avoid errors, the test should be repeated when tuning the receiver to another station, sufficiently distant from the first one in frequency.
Measuring inductances using the voltmeter-ammeter method
Voltmeter - ammeter method used for measuring relatively large inductances when the measuring circuit is powered from a low frequency source F = 50...1000 Hz.
The measurement diagram is shown in Fig. 3, A. The impedance Z of the inductor is calculated by the formula
Z = (R2+X2) 0.5 = U/I
based on the readings of alternating current devices V ~ and mA ~. The upper (according to the diagram) terminal of the voltmeter is connected to the point A at Z<< Z в и к точке b at Z >> Z a, where Z in and Z a are the total input resistances of the voltmeter V ~ and milliammeter mA ~, respectively. If the losses are small, i.e. R<< X = 2*π*F*L x , то измеряемая индуктивность определяется формулой
L x ≈ U/(2*π*F*I).
In order to reduce their size, large inductance coils are usually made with steel cores. The presence of the latter leads to a nonlinear dependence of the magnetic flux on the current flowing through the coil. This relationship becomes especially complex for coils operating with bias, through the windings of which both alternating and direct currents flow. Therefore, the inductance of coils with steel cores depends on the value and nature of the current flowing through them. For example, with a large constant current component, magnetic saturation of the core occurs and the inductance of the coil sharply decreases. In addition, the permeability of the core and the inductance of the coil depend on the frequency of the alternating current. It follows that the measurement of the inductance of coils with steel cores must be carried out under conditions close to their operating conditions. In the diagram in Fig. 3, A this is ensured by supplementing it with a direct current circuit, shown by the dashed line. The required bias current is set by rheostat R2 according to the readings of a DC milliammeter mA. Separating capacitor C and inductor Dr separate the DC and AC power circuits, eliminating mutual influence between them. AC devices used in this circuit should not respond to direct components of the current or voltage they measure; for a voltmeter V ~ this is easily achieved by connecting a capacitor with a capacity of several microfarads in series with it.
Rice. 3. Schemes for measuring inductance using the voltmeter - ammeter method.
Another version of the measuring circuit, which allows you to do without an AC milliammeter, is shown in Fig. 3, b. In this circuit, rheostats R1 and R2 (they can be replaced by potentiometers connected in parallel with power supplies) set the required test mode for alternating and direct current. In switch position 1 IN The voltmeter V ~ measures the alternating voltage U 1 on the coil L x. When the switch is moved to position 2, the value of the alternating current in the circuit is actually controlled by the voltage drop U 2 across the reference resistor R o. If the losses in the coil are small, i.e. R<< 2*π*F*L x , то измеряемую индуктивность можно рассчитать по формуле
L x ≈ U1*R o /(2*π*F*U 2).
Bridge method for measuring the parameters of inductors. Universal measuring bridges
Bridges intended for measuring the parameters of inductors are formed from two active resistance arms, an arm with the measurement object, the resistance of which is generally complex, and an arm with a reactive element - a capacitor or inductor.
Rice. 4. Circuit of a store bridge for measuring inductances and loss resistances.
In store-type measuring bridges, it is preferred to use capacitors as reactive elements, since in the latter, energy losses can be made negligible, and this contributes to a more accurate determination of the parameters of the coils under study. The diagram of such a bridge is shown in Fig. 4. The adjustable element here is a capacitor C2 of variable capacity (or a store of capacitances), shunted by a variable resistor R2; the latter serves to balance the phase shift created by the loss resistance R x in the inductance coil L x . Applying the amplitude equilibrium condition (Z 4 Z 2 = Z 1 Z 3), we find:
(R x 2 + (2*&pi*F*L x) 2) 0.5: ((1/R 2) 2 + (2*&pi*F*C 2) 2) 0.5 = R 1 R 3 .
Since the phase angles are φ1 = φ3 = 0, the phase equilibrium condition (φ4 + φ2 = φ1 + φ3) can be written as the equality φ4 + φ2 = 0, or φ4 = -φ2, or tg φ4 = -tg φ2. Considering that for an arm with L x the formula (tg φ =X/R) is valid, and for an arm with a capacitance C 2 the formula (tg φ =R/X) is valid for a negative value of the angle φ2, we have
2*&pi*F*L x / R x = 2*&pi*F*C 2 R 2
Solving the above equations together, we get:
L x = C 2 R 1 R 3 ; (1)
R x = R 1 R 3 / R 2 . (2)
From the last formulas it follows that capacitor C2 and resistor R2 can have scales for directly assessing the values of L x and R x, and the amplitude and phase adjustments made by them are mutually independent, which allows you to quickly balance the bridge.
To expand the range of measured values, one of the resistors R1 or R3 is usually made in the form of a resistance store.
If it is necessary to measure the parameters of coils with steel cores, the bridge diagram in Fig. 4 is supplemented by a constant voltage source U o, a rheostat R o and a direct current milliammeter mA, which serve to regulate and control the bias current, as well as the inductor Dr and capacitor C, separating the circuits of the alternating and direct current components.
Rice. 5. Circuit of a store bridge for measuring inductances and quality factors
In Fig. Figure 5 shows a diagram of another version of the magazine bridge, in which capacitor C2 has a constant capacitance, and resistors R1 and R2 are taken as variable. Expansion of the measurement range is carried out by including resistors R3 of various ratings in the bridge. From formulas (1) and (2) it follows that the amplitude and phase adjustments in this circuit turn out to be interdependent, therefore balancing the bridge is achieved by alternately changing the resistances of resistors R1 and R2. Inductance L x is assessed on the scale of resistor R1, taking into account the multiplier determined by the setting of the switch IN. The reading on the resistor R2 scale is usually made in the Q-values of the coils
Q L = 2*π*F*L x /R x = 2*π*F*C 2 R 2 .
at frequency F of the power source. The validity of the last formula can be verified if the left and right sides of equality (1) are divided into the corresponding parts of equality (2).
With the data indicated on the diagram, the measuring bridge allows you to measure inductances from approximately 20 μH to 1, 10, 100 mH; 1 and 10 H (without steel cores) and quality factor up to Q L ≈ 60. The power source is a transistor generator with an oscillation frequency F ≈ 1 kHz. The imbalance voltage is amplified by a transistor amplifier loaded onto TF telephones. A double T-shaped RC filter, tuned to a frequency of 2F ≈ 2 kHz, suppresses the second harmonic of source oscillations, which facilitates balancing of the bridge and reduces measurement error.
Bridge meters of inductance, capacitance and active resistance have a number of identical elements. Therefore, they are often combined in one device - a universal measuring bridge. Universal high-precision bridges are based on store circuits such as those shown in Fig. 5. They contain a constant voltage source or rectifier (powering the R x measurement circuit), a low-frequency generator with an output power of several watts, a multi-stage unbalance voltage amplifier loaded on a magnetoelectric galvanometer; the latter, when measuring active resistances, is included directly in the measuring diagonal of the bridge. The required measurement circuit is formed using a rather complex switching system. In such bridges, logarithmic type indicators are sometimes used, the sensitivity of which drops sharply if the bridge is not balanced.
Rice. 6. Scheme of a universal rheochord bridge for measuring resistance, capacitance and inductance
Much simpler are universal slide-type bridges, which measure the parameters of radio components with an error of the order of 5-15%. A possible diagram of such a bridge is shown in Fig. 6. For all types of measurements, the bridge is powered by a voltage with a frequency of approximately 1 kHz, which is excited by a transistor generator made according to an inductive three-point circuit. The balance indicator is a high-impedance TF telephone. Resistors R2 and R3 are replaced by a wire rheochord (or, more often, a regular potentiometer), which allows the bridge to be balanced by smoothly changing the resistance ratio R2/R3. This ratio is measured on the slider scale, the range of readings of which is usually limited to the extreme values of 0.1 and 10. The measured value is determined with a balanced bridge as the product of the reading on the slider scale and the multiplier determined by the setting of switch B. Each type and limit of measurement corresponds to inclusion in the bridge circuit the corresponding supporting element of the required rating - capacitor C o (C1), resistor R o (R4) or inductor L o (L4).
A feature of the scheme under consideration is that the measured elements R x and L x are included in the first arm of the bridge (with support elements R o and L o located in the fourth arm), and C x, on the contrary, in the fourth arm (with C o - in the first shoulder). Thanks to this, the assessment of all measured quantities is carried out using similar formulas like
A X = A o (R2/R3),
where A x and A o are the values of the corresponding measured and reference elements.
Variable resistor R5 serves to compensate for phase shifts and improve bridge balancing when measuring inductances. For the same purpose, a variable resistor of small resistance is sometimes included in the circuit of the reference capacitor C about the measurement limit of large capacitances, which often have noticeable losses.
In order to eliminate the influence of the operator's hand, the slider engine is usually connected to the body of the device.
Resonant inductance meters
Resonance methods make it possible to measure the parameters of high-frequency inductors in the range of their operating frequencies. The measurement schemes and methods are similar to those used for resonant measurements of capacitor capacitances, taking into account, of course, the specifics of the measurement objects.
Rice. 7. Resonant circuit for measuring inductances with reading on the generator scale
The inductor under study can be included in a high-frequency generator as an element of its oscillatory circuit; In this case, the inductance L x is determined based on the readings of a frequency meter that measures the oscillation frequency of the generator.
More often, the L x coil is connected to a measuring circuit connected to a source of high-frequency oscillations, for example a generator (Fig. 2) or the input circuit of a radio receiver tuned to the frequency of a broadcasting station (Fig. 8). Let us assume that the measuring circuit consists of a coupling coil L with a tuning core and a variable capacitor C o.
Rice. 8. Scheme for measuring capacitances using the resonant method using a radio receiver
Then the following measurement technique is applicable. The measuring circuit at the maximum capacitance C o1 of the capacitor C is adjusted to resonance with the known frequency f of the oscillation source by adjusting the inductance L. Then the coil L x is connected to the circuit in series with its elements, after which the resonance is restored by reducing the capacitance Co to a certain value Co2. The measured inductance is calculated using the formula
L x = * (C o1 -C o2)/(C o1 C o2).
In wide-range resonant meters, the measuring circuit is made up of a reference capacitor CO and a coil under study L x. The circuit is connected inductively, or more often through a small capacitor C 1 (Fig. 7 and 9) with a high-frequency generator. If the generator oscillation frequency f 0 is known, corresponding to the resonant tuning of the circuit, then the measured inductance is determined by the formula
L x = 1/[(2*π*f o) 2 *C o ]. (3)
There are two options for constructing measuring circuits. In the circuits of the first option (Fig. 7), the capacitor C o is taken with a constant capacitance, and resonance is achieved by changing the settings of the generator operating in a smooth frequency range. Each value of L x corresponds to a certain resonant frequency
f 0 = 1/(2*π*(L x C x) 0.5), (4)
therefore, the generator loop capacitor can be equipped with a scale reading in L x values. With a wide range of measured inductances, the generator must have several frequency subranges with separate scales for estimating L x in each subrange. If the device uses a generator that has a frequency scale, then tables or graphs can be drawn up to determine L x from the values of f 0 and C o.
To eliminate the influence of the coil’s own capacitance C L on the measurement results, the capacitance C o must be large; on the other hand, it is desirable to have the capacitance C o small in order to ensure, when measuring small inductances, a sufficiently large ratio L x /C o, necessary to obtain noticeable indicator readings at resonance. In practice, they take C o = 500...1000 pF.
If a high-frequency generator operates in a limited frequency range that is not divided into subranges, then several switchable capacitors C o are used to expand the limits of inductance measurement; if their capacities differ by a factor of 10, then at all limits the assessment of L x can be made on the same generator scale using multipliers to it that are multiples of 10. However, such a scheme has significant drawbacks.
The measurement of relatively large inductances having a significant intrinsic capacitance C L occurs at the limit with a small capacitance C o, and, conversely, the measurement of small inductances is carried out at the limit with a large capacitance C o with an unfavorable ratio L x / C o and a low resonant voltage on the circuit.
Rice. 9. Resonant circuit for measuring inductances with reading on the scale of the reference capacitor
In resonant meters, the circuits of which are made according to the second option (Fig. 9), inductances are measured at a fixed generator frequency f 0 . The measuring circuit is tuned to resonance with the frequency of the generator using a variable capacitor C o, the scale of which, in accordance with formula (3), can be read directly in L x values. If we denote by C m and C n the maximum and initial capacitance of the circuit, respectively, and by L m and L n the maximum and smallest values of the measured inductances, then the measurement limits of the device will be limited by the ratio
L m / L n = C m / C n.
Typical variable capacitance capacitors have a capacitance overlap of approximately 30. In order to reduce the error when measuring large inductances, the initial capacitance C n of the circuit is increased by including an additional capacitor C d in the circuit, usually of the tuning type.
If we denote by ΔС o the greatest change in the capacitance of the capacitor C o, equal to the difference in its capacitances at the two extreme positions of the rotor, then to obtain the selected ratio L m / L n the circuit must have an initial capacitance
C n = ΔC o: (L m / L n -1). (5)
For example, with ΔC o = 480 pF and the ratio L m / L n = 11, we obtain C n = 48 pF. If the values of C n and L m / L n in the calculation are the initial data, then it is necessary to use a capacitor C o, which has a capacitance difference
ΔC o ≥ C n (L m /L n -1).
For large values of C n and L m / L n, it may be necessary to use a double or triple block of variable capacitors.
The frequency f 0 at which the generator must operate is determined by formula (4) when substituting into it the values L m and C n or L n and C m. To expand the overall measurement range, the generator is operated at several switchable fixed frequencies. If adjacent frequencies of the generator differ by a factor of 10 0.5 ≈ 3.16, then at all limits you can use the general scale of capacitor inductance C o with multipliers to it that are multiples of 10 and determined by setting the frequency switch (Fig. 9). Smooth overlapping of the entire range of measured inductances is ensured when the ratio of the circuit capacitances C m / C n ≥ 10. If the capacitor Co is of logarithmic type, then the inductance scale is close to linear.
Instead of a fixed frequency generator, you can use a measuring generator with a smooth frequency change, which is set depending on the required limit for measuring inductances.
Resonant circuits for measuring inductance and capacitance are often combined in one device, since they have a number of identical elements and a similar measurement technique.
Example. Calculate a resonant inductance meter operating according to the circuit in Fig. 9, for a measurement range of 0.1 μH - 10 mH when using a dual block of variable capacitors, the capacitance of the sections of which can be changed from 15 to 415 pF.
Solution
1. The largest change in the circuit capacitance ΔС o = 2*(415-15) = 800 pF.
2. Select the ratio L m / L n = 11. Then the device will have five measurement limits: 0.1-1.1; 1-11; 10-110; 100-1100 µH and 1-11 mH.
3. According to (5), the circuit must have an initial capacitance C n = 800/10 = 80 pF. Taking into account the initial capacitance of the capacitor block, equal to 30 pF, we include in the circuit a tuning capacitor C d with a maximum capacitance of 50...80 pF.
4. Maximum circuit capacitance C m = C n + ΔC o = 880 pF.
5. According to (4), at the first measurement limit the generator must operate at a frequency
f 01 = 1/(2*π*(L n C m) 0.5) ≈ 0.16*(0.1*10^-6*880*10^-12) ≈ 17 MHz.
For other measurement limits we find, respectively: f 02 = 5.36 MHz; f 03 = 1.7 MHz; f 04 = 536 kHz; f 05 = 170 kHz.
6. We carry out the inductance scale for the measurement limit of 1-11 μH.
Q-meters (kumeters)
Instruments designed to measure the quality factor of elements of high-frequency circuits are often called kumeters. The action of cometers is based on the use of resonant phenomena, which allows the measurement of quality factor to be combined with the measurement of inductance, capacitance, natural resonant frequency and a number of other parameters of the elements under test.
Kumeter, a simplified diagram of which is shown in Fig. 10, contains three main components: a high-frequency generator, a measuring circuit and a resonance indicator. The generator operates over a wide, smoothly overlapping frequency range, for example from 50 kHz to 50 MHz; this allows many measurements to be carried out at the operating frequency of the elements under test.
The inductor under study L x , R x through terminals 1 and 2 is connected to the measuring circuit in series with the reference capacitor of variable capacitance C o and the coupling capacitor C 2 ; the capacity of the latter must satisfy the condition: C 2 >> C o.m, where C o.m is the maximum capacitance of the capacitor C o. Through a capacitive divider C 1, C 2 with a large division coefficient
N = (C 2 + C 1)/C 1
A reference voltage U about the required high frequency f is introduced into the circuit from the generator. The current arising in the circuit creates a voltage drop U C across the capacitor C o, which is measured by a high-frequency voltmeter V2.
The input resistance of voltmeter V2 within the operating frequencies of the meter must be very high. If the sensitivity is sufficiently high, the voltmeter is connected to the measuring circuit through a capacitive voltage divider, the input capacitance of which is taken into account as a component of the initial capacitance of the capacitor C o. Since all the capacitors that are part of the measuring circuit have very small losses, we can assume that the active resistance of the circuit is mainly determined by the loss resistance R x of the coil under study.
Rice. 10. Simplified diagram of the kumeter
By changing the capacitance of the capacitor C o, the measuring circuit is tuned into resonance with the generator frequency f according to the maximum readings of the voltmeter V2. In this case, a current I p ≈ U o /R x will flow in the circuit, creating a voltage drop across the capacitor
U C = I p /(2*π*f*C o) ≈ U o /(2*π*f*C o R x).
Considering that at resonance 1/(2*π*f*С о) = 2*&pi*f*L x , we find
UC ≈ U o (2*π*f*L x)/R x = U o Q L ,
where Q L = (2*π*f*L x)/R x is the quality factor of the coil L x at frequency f. Consequently, the readings of the voltmeter V2 are proportional to the quality factor Q L. At a fixed voltage U o, the voltmeter scale can be linearly calibrated in the values Q L ≈ U C /U o. For example, with U o = 0.04 V and the measurement limit of the voltmeter U p = 10 V, the voltages at the voltmeter input 2, 4, 6, 8 and 10 V will correspond to the quality factor Q L equal to 50, 100, 150, 200 and 250.
The rated voltage U o is set by adjusting the mode of the generator output stage. This voltage is monitored according to the readings of a high-frequency voltmeter V1, which measures the voltage U 1 = U o N at the generator output. For example, if the quality factor scale of voltmeter V2 is made at a voltage Uo = 0.04 V, and the division coefficient N = 20, then the voltage at the generator output must be maintained at U x = 0.04 * 20 = 0.8 V. The measurement limit of voltmeter V1 must be slightly exceed the calculated voltage value U 1 and is equal to, for example, 1 V.
Increasing the upper limit for measuring quality factors is achieved by reducing the voltage U o to a value several times less than the nominal one. Let us assume that at a voltage U o = 0.04 V, a direct reading of the quality factor is provided to the value Q L = 250. If we reduce the voltage U o by half, to 0.02 V, then the voltmeter needle V2 will deviate to the full scale at the quality factor Q L = U p /U o = 10/0.02 = 500. Accordingly, to increase the upper measurement limit by four times, to the value Q L = 1000, measurements should be carried out at a voltage U o = 40/4 = 10 mV.
The voltage U o can be reduced to the required value in two ways: by changing the division coefficient N by switching capacitors C 1 of different ratings or by adjusting the output voltage U 1 of the generator. For the convenience of measuring high quality factors, voltmeter V1 (or a division factor switch) is equipped with a scale (marking), the reading on which, characterizing the degree of reduction in voltage U o compared to its nominal value, is a multiplier to the quality factor scale of voltmeter V2.
To check the operation of the meter and expand its capabilities, support coils L o with known inductance and quality factor are used. Usually there is a set of several replaceable coils L o, which, together with a variable capacitor C o, provide resonant tuning of the measuring circuit within the entire range of operating frequencies of the generator.
When measuring quality factor of inductors Q L 10-15 minutes before starting work, turn on the power to the device and tune the generator to the required frequency. After warming up, the voltmeters V1 and V2 are set to zero. The coil under test is connected to terminals 1 and 2. By gradually increasing the output voltage of the generator, the voltmeter needle V1 is deflected to the nominal level. The capacitor Co tunes the circuit into resonance with the frequency of the generator. If at the same time the needle of the voltmeter V2 goes beyond the scale, the output voltage of the generator is reduced. The value of the quality factor Q L is determined as the product of readings on the quality factor scale of the voltmeter V2 and on the multiplier scale of the voltmeter V1.
Quality factor of the oscillatory circuit Q K is measured in the same order by connecting the circuit coil to terminals 1 and 2, and its capacitor to terminals 3 and 4. In this case, the capacitor C o is set to the minimum capacitance position. If the capacitor of the circuit under study has a variable capacitance, then it is used to tune the circuit into resonance at the required generator frequency f; if this capacitor is constant, then resonant tuning is carried out by changing the frequency of the generator.
Measuring with a meter coil inductance L x is produced in the manner discussed above in connection with the diagram in Fig. 9. The generator is tuned to the reference frequency, selected according to the table depending on the expected value of L x. The coil under test is connected to terminals 1 and 2. The measuring circuit is adjusted to resonance with a capacitor C o, on a special scale of which the value of L x is assessed, taking into account the division value indicated in the table. At the same time, by varying the contour parameters, it is possible to determine coil's own capacity C L . For two arbitrary values of capacitances C 01 and C 02 of the capacitor C, by changing the generator settings, the resonant frequencies of the circuit f 1 and f 3 are found. Required capacity
C L = (C 02 f 4 2 -C 01 f 1 2) : (f 1 2 -f 2 2)
Measuring containers with a meter is performed using the substitution method. The capacitor under test C x is connected to terminals 3 and 4, and one of the support coils L o is connected to terminals 1 and 2, providing resonant tuning of the circuit in the selected frequency range. At the same time, you can determine the loss tangent (quality factor) of the capacitor:
tan δ = 1/(2*π*f*C x R p)
(where R p is the loss resistance). To do this, with two values of capacitances C 01 and C 02, corresponding to the resonant settings of the circuit without capacitor C x and when the latter is connected, find the quality factors of the circuit Q 1 and Q 2, and then perform the calculation using the formula
tg δ = Q 1 Q 2 /(Q 1 -Q 2) * (C 01 -C 02)/C 01
If necessary, the kumeter generator can be used as a measuring generator, and electronic voltmeters can be used to measure voltages in a wide frequency range.
