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A Poor Man’s Q-Meter By Maurie Findlay, MIEAust This simple unit is made from a few inexpensive components and allows you to make measurements which usually require an expensive Q-meter. In conjunction with a signal generator and an electronic voltmeter, inductance and “Q” can be measured quite accurately. E XPERIMENTERS AND even professionals setting up a test bench have to think hard before buying test instruments. Depending on the special interest, items such as a multimeter, regulated power supply, counter, oscilloscope, RF and AF signal generators would come high on the list. Money can be saved by building test gear described in SILICON CHIP over the years. Sometimes out-of-date 46  Silicon Chip equipment from schools and government departments can be overhauled and brought into service. But for most people, the purchase of a Q-meter would probably be pretty low on the priority list. There are at least two reasons for this. Inexpensive hand-held bridges can measure inductance reasonably accurately, provided the values are not too small (say below 10 µH). Second, the selective components used in modern equipment usually come in block form such as ceramic, crystal or mechanical filters with the characteristics specified by the manufacturer. No longer does the designer have to specify the inductance and Q of a whole series of coils to make up a filter for, say, the intermediate frequency (IF) section of a receiver. On the other hand, inductances to a fraction of a µH are used in the signal frequency circuits of both transmitters siliconchip.com.au and receivers for filters, tuning, coupling and decoupling circuits. Inductors used for coupling between tuned circuits and to active devices are usually quite critical but they are not adjustable. So this discussion is about a simple test jig which, when used in conjunction with a signal generator and an electronic voltmeter, allows the inductance and Q of small coils to be measured accurately by resonance with a known value capacitor. It comes into its own when dealing with inductors below about 10µH. It can easily be adapted to measure a range of inductance by altering the value of the capacitor. Most readers will regard this as an ideas article rather than a constructional project to be copied component for component. The model illustrated is just one of many ways the basic idea can be used. Now let’s get down to the principles and then the practice. When an inductor is placed in parallel with a capacitor to form a tuned circuit, the resonant frequency is given by: where f, L and C are in the basic units of Hertz, Henries and Farads. If we know f and C, the equation can be rearranged to give the value of L in microhenries (µH) when C is in picofarads (pF) and the frequency in megahertz (MHz). C is known and fixed. We vary the frequency and calculate L. This can be done from the formula, or more conveniently from a graph plotting inductance against frequency. For convenience, we present graphs for C = 50pF, 200pF and 500pF. C is the value of the capacitor which effectively appears between the “HIGH” and “LOW” terminals of the test jig (see Fig.1) and is made up of two capacitors in series, the one connecting to the “LOW” terminal being about 10 times the value of the capacitor connecting to the “HIGH” terminal. The accuracy of the readings depends on the accuracy of the latter. Mica and polystyrene capacitors can be obtained with a 1% tolerance but these days you won’t find such items at every electronics store! In general terms, ceramic capacitors are not suitable for this job. This siliconchip.com.au With less than a dozen components, a digital multimeter and practically any RF signal generator, you can measure Q and inductance very easily. The old-style point-to-point wiring is housed in a shielded metal box. capacitor is the only critical component required for the project. We have found capacitors with 1% tolerance in ex-military equipment. Alternatively, you may have to ask a favour of a friend with access to laboratory test equipment. It is unlikely that you will be able to get the values of C required with a single capacitor and so various combinations of serial and parallel may be needed. The value of two capacitors in series is calculated by multiplying the two values and dividing this figure by the sum of the two values (remember resistors in parallel?). For 220pF in series with 2000pF this works out to be 198.2 pF. Not bad but you can always select a nominal 2000pF capacitor which is a little on the high side. For most purposes, the reading from the graph will be accurate enough. If you need greater accuracy, calculate the value of inductance from the formula. For measurements to be made, it is necessary to excite the tuned circuit formed by the fixed C and the unknown L and measure its response. To do this, some of the RF energy must be fed into this tuned circuit. It is not possible to do this without having some effect on both the frequency and the losses of the tuned circuit. In practice, the errors are acceptable provided the frequency and natural Q of the tuned circuit are not too high. Some expensive commercial Qmeters go to a great deal of trouble to reduce errors. With the simple techniques used here, the accuracy Fig.1: because frequency generation is undertaken by a signal generator and readout by a digital voltmeter, the circuit is delightfully simple. July 2004  47 Inside the box: four capacitors, three resistors, a diode and a switch make up the total component count. BNC connectors have been used for the oscillator input and multimeter output but these are not mandatory. is acceptable for most purposes up to about 300MHz and a Q of 200. Standard practice for Q-meters is to excite the tuned circuit by inserting a small value, non-inductive resistor in series with the inductor under test. The output of the signal generator is applied across this resistor, sometimes through an RF transformer. The instrument measures the RF current through the resistor and the Q (magnification factor) can be measured by an RF voltmeter across the circuit. The simple system used here couples into the tuned circuit partly by reactive and partly by resistive components. It fits in with the usual signal generator that is designed to feed into 50Ω. Modern generators usually have a maximum output of 1V RMS and the older types 100mV with x2 switching if used without amplitude modulation. High Q & low Q The suggested circuit shows a switch labelled “HIGH Q” and “LOW Q”. This switch is left in the “HIGH Q” position if you have a high output signal generator and a sensitive voltmeter in order to keep the coupling Fig.2: in many cases, you’ll be able to read values straight off these graphs without having to resort to formulas. We’ve shown three easily-arranged capacitance values. 48  Silicon Chip between the generator and the tuned circuit low. However, with low Q tuned circuits and low output signal generators, you can at least get a reading, even if it is less accurate. Don’t worry about the signal generator not being correctly terminated. In this case, it doesn’t matter. Again, looking at the suggested circuit (Fig.1), the detector is in a shunt diode arrangement using a BA482 lowcapacitance, low-loss silicon diode. There are other diodes which will do the job just as well. The output of the detector is fed to a connector and then to a DMM set to a DC scale. Most DMMs have an input resistance of 10MΩ or greater. The older valve electronic voltmeters usually have a 0-1.5V scale, while the most sensitive range for modern DMMs may be 200mV. The net result of losses brought about by the exciting signal and the loading of the detector is that the measured Q of very efficient inductors will be less than the true value. The same applies to expensive commercial Q-meters, although some of the best of them do have built-in circuits to partially compensate. Because we don’t know the precise value of the RF used to excite the tuned circuit, the value of Q has to be measured by indirect means. Use is made of the universal selectivity curve (see Terman “Electronic and Radio Engineering” and others). The curve has the same general shape, regardless of the value of Q and the siliconchip.com.au frequency and can be of great value when designing tuned filters with special characteristics. For the purposes of measuring Q we are interested in the response at three frequencies. These are: the maximum; the frequency lower than the maximum at which the response is 0.707 (-3dB); and the frequency above the maximum at which the response is 0.707. The difference between the two -3dB frequencies is the bandwidth. The Q of the circuit is the centre frequency divided by the bandwidth. If you are making a lot of measurements, it soon becomes a matter of routine and given a pocket calculator, you can work very quickly. There will be cases where you do not need to know the precise value of Q and you can zip through a series of readings by noting that the reading on the voltmeter is above a certain value. The Q-meter jig pictured here was originally set up to check the inductors for low-pass filters used in HF radio transceivers operating between 2MHz and 20MHz. Inductance values between about 0.2µH and 3.0µH were used and the values needed to be within about 5%. A parallel capacitance of 200pF brought the resonant frequencies within the range of even the older HF signal generators. To cover a wide range of inductance values, there is always the possibility of installing switched capacitors or a calibrated variable capacitor but the jig is so simple that two or more separate units may be just as easy. For very small value inductors, as may be used in VHF equipment, a switched arrangement may not be practical. Having made up the jig in a form that suits your purpose, find a low-Q inductor, ideally of known value, and work out the resonant frequency. With the signal generator and voltmeter connected, tune the signal generator for maximum indication. The signal generator should be set for maximum output. Note the reading of the DMM. If too low for convenience you can reduce the value of the 4.7kΩ resistor as required. The lower the value the greater the reduction in the measured Q. Similarly, you can increase the reading of the voltmeter slightly by reducing the value of the series resistor, marked 2.2MΩ on the circuit, to about 1MΩ. Using a 47Ω resistor in series with a 50Ω output signal generator (ie, the switch in the “LOW Q” position), a coil with a true Q of 250 will measure only about 50. If you are only concerned with the inductance value, this may not matter. Having adjusted the set-up to suit your instruments, the routine for measurement goes like this: Inductance · Connect voltmeter and signal gen- erator; · Connect unknown inductor; · Tune signal generator for maximum meter deflection and note the frequency; and · Read the inductance from the graph for the corresponding value of C or calculate the inductance from the formula. Q value · Using the signal generator’s atten- uator, reduce the output by 3dB; · Note the meter reading; · Return the signal generator’s attenuator to the setting for full output; · Adjust the signal generator’s frequency higher, to the point where the meter reading drops to the -3dB point; · As above but on the low-frequency side. Subtract this frequency from the one above to obtain the bandwidth; · Q is then the centre frequency divided by the bandwidth. If your signal generator has a digital readout or you can connect a counter to read frequency, very good accuracy can be obtained. SC Happy measuring ! 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