Simple LC meter

This very simple LC meter can provide capacitance and inductance measurement, and some more things:

• capacitance measurement without removing capacitors from circuit boards;
• inductance measurement;
• frequency measurement of TTL signals;
• Q factor of capacitors;
• permeability of cores;
• Q factor of inductors;
• detecting short circuit of windings (it works as a shorted turns tester).

This is parameters of the LC meter:

Power supply voltage, V	4.3
Max. current consumption, mA	45
Measuring range of capacitance, uF	80*10-6...20*103
Measuring range of inductance, H	2.5*10-6...40
Measuring range of frequency, Hz	1..16*106
Voltage across probes, V (for capacitance meter)	0.35
Voltage across probes, V (for inductance meter)	10
Minimum Q-factor of inductance	11

The circuit diagram of this LC meter is shown in figure 1. Two integrated circuits DD1 and DD2 (74HC00) forms a generator, which frequency is determined by capacitor Cx or inductor Lx to be measured. Another two integrated circuits, DD3 and DD4 (CD74HCT4040) provide frequency division by 2¹²*2¹² = 2²⁴ = 16777216. The display of the LC meter has 25 stages, each stage is differ from the nearest stage in 2 times. How to read this display? The LED, which flashing frequency is close to 1 Hz is the reading of the LC meter.

LED	C	L	F
VD1	25 mF	40 H	1 Hz
VD2	12 mF	20 H	2 Hz
VD3	6 mF	10 H	4 Hz
VD4	3 mF	5 H	8 Hz
VD5	1.5 mF	2.5 H	16 Hz
VD6	800 μF	1.3 H	32 Hz
VD7	400 μF	625 mH	64 Hz
VD8	200 μF	320 mH	128 Hz
VD9	100 μF	160 mH	256 Hz
VD10	50 μF	80 mH	512 Hz
VD11	24 μF	40 mH	1 kHz
VD12	12 μF	20 mH	2 kHz
VD13	6 μF	10 mH	4 kHz
VD14	3 μF	5 mH	8 kHz
VD15	1.5 μF	2.5 mH	16 kHz
VD16	760 nF	1.2 mH	32 kHz
VD17	380 nF	610 μH	64 kHz
VD18	185 nF	300 μH	128 kHz
VD19	90 nF	150 μH	256 kHz
VD20	43 nF	80 μH	512 kHz
VD21	19 nF	40 μH	1 MHz
VD22	7 nF	20 μH	2 MHz
VD23	1 nF	10 μH	4 MHz
VD24	80 pF	5 μH	8 MHz
VD25	-	2.5 μH	16 MHz
Table 1.

Capacitance measurement

Discharge the capacitor to be measured. Open the switch S1 (switch it in "C" position). There is three ways to provide the measurement, they have different precision.

Method 1. Connect the probe tips to the capacitor (it may not be removed from a circuit board) and find a LED flashing with the frequency about 1 Hz. Read value of the capacitor near of the LED (see Table 1, second row).

Method 2. To get more precision value, do the same as said in the method 1, but find the LED with the flashing frequency more than 1 Hz, count the number of flashes for 10 seconds, and calculate the frequency of flashing - divide the number of flashes by 10. Then divide the capacitance value, shown for this LED by the frequency. Here is the formula:

Cx = C * T / N,[0]

where
Cx - the result;
C - value of the capacitance for the current LED (see the table 1);
T - time of measurement, in this case it is 10 seconds, but it can be longer if necessary;
N - number of flashes counted for the time T.

This is an example: let the LED VD14 is flashing with the frequency more than 1 Hz. In 10 seconds it gives 33 flashes, therefore 33/10 = 3.3 Hz. The value of capacitance shown for this LED is 3 μF. Then 3/3.3 = 0.9 μF.

By the formula [0], the capacitance is:

Cx = C * T / N = 3 * 10 / 33 = 0.9 μF

Method 3. Use an oscilloscope or a frequency meter to get even more precision value of measured parameters. By the way, using an oscilloscope, it is possible to measure the Q factor of capacitors. Connect the probes to the capacitor to be measured, and connect to the same probes the oscilloscope or frequency meter. If this is capacitor with high Q factor, you'll see the waveform as shown in Fig. 2(A). For any capacitor with low Q factor the waveform will look like shown in Fig 2(B). Determine the period T and find out the capacitance of the capacitor by this formula:

Cx = (T / 40) - 5 * 10^-9[1]

where
Cx - the capacitance, in Farads,
T - time in seconds.

Inductance measurement

An inductance also can be measured by three ways.

Method 1. This is the same as the method 1 for capacitors, except you have to switch S1 into "L" position.

Method 2. The same as the method 1 for capacitors, also switch the S1 into "L" position.

Method 3. This method is similar to the third method for capacitance measurement, the inductance can be calculated using this formula:

Lx = T * 40,[2]

where
Lx - the inductance in Henry,
T - time in seconds.

The waveforms for inductance coils with high and low Q factor are shown in Fig. 3(A) and Fig. 3(B) respectively.

If capacitors and inductors are low Q factor components, then result of measurements will have errors - the lower Q factor, the higher error level.

Frequency measurement

This LC meter can provide frequency measurement for TTL signals, but the measuring signal source must be galvanic isolated from the device. Turn the switch S1 into "C" position. Connect one probe to the ground, and the second to the signal source. Take a reading against a LED, which flashing frequency is about 1 Hz. To get more precise results, use a method, similar to method 2 of capacitance measurement.

How to measure the Q factor of capacitors

It takes an oscilloscope to measure the Q factor of capacitors.

Method 1. Connect a capacitor to be measured to probes, and connect the oscilloscope to it. If the waveform looks like shown on Figure 2(B), it means that the capacitor has a low Q factor, and it can be calculated. The capacitor can be represented as a capacitor and a resistor. Then Q factor can be found as follows:

Q = Xc/Rc = 2*Π*f*C/Rc, [3]

where
Xc - capacitive reactance of the capacitor [Ω];
Rc - the series resistance of the capacitor [Ω];
Π = 3.14159;
f - frequency at which the capacitor operates [Hz];
C - capacitance of the capacitor [F].

For this LC meter:

Rc = Un/0.03 [Ω] [4]

Where Un - the voltage shown in Figure 2(B), its value can be measured with an oscilloscope. If connect LC meter to the capacitor, we can get the period T (using the series resistance of the capacitor Rc):

T = 3.33*(12 - Rc)*(C + 5 * 10^-9) [seconds] [5]

If in this formula Rc = 0, then we get the transformed formula 1.

Method 2. Using the LC meter, find out the capacity of a capacitor. If measured value is more than 2 times less than the value printed on the capacitor, it means that the capacitor has very high series resistance Rc, therefore the capacitor has very low Q factor. Then the series resistance Rc can be found by using the formula [5]. The results are shown in the table below:

N, times	2	4	8	16	32	64
Rc, Ω	6	9	10.5	11.25	11.63	11.81
Table 2

In the upper row of the table 2 are multipliers, they are a ratio between a capacitance value printed on the capacitor, and the measured value. The lower row shows the series resistance Rc for a capacitor. For example, the real capacitance of a capacitor is 10 nF, and the measured capacitance is 2.5 nF, then Rc = 9 Ω

How to measure the Q factor of inductance coils

Using this device, find out inductance of a coil. Use an ammeter, find out resistance R of this coil. Calculate inductive reactance of the coil at the frequency f with this formula:

X_L = 2*Π*f*L, [Ω][6]

where
X_L - inductive reactance of the coil, [Ω];
Π = 3.14159;
f - operating frequency, [Hz];
L - inductance of the coil, [H].

The Q factor of the inductance coil can be calculated with this formula:

Q = X_L/R. [7]

The sensitivity of this LC meter allows to find out the Q factor for Q > 11.

How to determine permeability of unknown cores

There is three type of cores (see Figure 4).

Formulas [9] and [10] are used for toroid cores, [11] and [12] - for Π-shaped cores, [13] and [14] - for E-shaped cores. All dimensions are in cm.

Wind no less than 15 turns on a core (for E-shaped core use its center console for winding) and measure its inductance using this LC meter. The permeability can be calculated using this formula:

Μ = (L * Lm) / (μ₀ * n² * Sm)[15]

where
L - inductance of the coil with the core, [H];
Lm - mean length of the flux path, [cm];
Sm - cross sectional area of the core, [cm²];
μ₀ - the absolute permeability of free space [μ₀ = 4*Π*10^-9 H/cm];
n - number of turns.

How to test windings for shorted turns

To detect shorted turns in a coil with cores, it takes to compare the measured inductance and the calculated inductance:

L = μ₀*μ_E * (n²*Sm )/ Lm, [16]

where
μ_E - the permeability of cores. If its value is unknown, it can be found as it was described earlier.

If the measured inductance is less than the calculated inductance in 2 and more times, therefore there is shorted turns in the windings.

Components

formulas [1, 2, 4, 5] are correct for LC meter with IC 74HC00 as DD1, DD2. In case using another ICs (7400, 74LS00 and other), all this formulas need to be corrected. It is important to use a fast IC, and when this IC is used, the voltage across probes shouldn't be higher than 0.3..0.4, to prevent p-n junction (of silicon and germanium devices) from opening. It will allow to measure capacitance of capacitors without removing them from circuit boards. Using some types of IC, it may take to install an additional capacitor C6 into circuit. Match its value, it may vary in range of 1 nF..0.01 μF. Without this capacitor some ICs may not start to oscillate. In some cases add a resistor R27 (match its value). All this can reduce upper operating range of the LC meter.

Any suitable binary counters can be use as DD3, DD4, the best choice is CD74HCT4040, because it is fast IC with 12 stages. It takes more ICs if a binary counter has less stages.

Warning! The supply voltage of this LC meter is 4.3 volts, the voltage is stabilized. It takes to modify formulas [1, 2, 4, 5] to use another value of supply voltage. It may take to change the supply voltage for other ICs than 74HC00. By changing the supply voltage, we can change the range of the LC meter. If the generator won't start, adjust the power supply voltage. For example, the generator circuit with the USSR IC 1533LA3 will oscillate only if the power supply is in range 2.6..4.0 V (the voltage across pins 7 and 14 of DD1, DD2 is 2.0..3.2 V).

LEDs VD1-VD25, used in this circuit are any suitable red LEDs. The diode VD26 protects the circuit from reverse polarity voltage.

The wires, connected to the probes must be as short as possible (10..20 cm), because their inductance can cause some measurement errors.

S. Volodzko, "Radio Amateur", December 2000.

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