Fullscreen HTML5Med Res (??MB)HTML4

We’ve published numerous LC meters that can measure inductance and capacitance, but you might need to know the quality factor (Q) of an inductor, not just its inductance. This Q Meter uses a straightforward circuit to measure the Q factor over a wide range, up to values of about 200. Q Meter T he history of Q Meters goes back to 1934, when Boonton developed the first Q Meter. The Q Meter is a somewhat neglected piece of test equipment these days. Hewlett Packard bought Boonton in 1959 and produced revised versions of their Q Meter. Does anyone still manufacture them? It seems not. You can find a few on the second-hand market; they fetch prices up to $3000. The HP 4342-A is an excellent unit and is a more modern version of the original Boonton design. My Q Meter design can’t come near the quality or accuracy of that HP unit. It is not designed as a laboratory instrument but will give Q measurements up to a value of about 200 with an accuracy of about 10%. Q&A So, what is Q, and why do we need to measure it? It is a measure of the dissipative characteristic of an inductor. High-Q inductors have low dissipation and are used to make finely-tuned, narrow-band circuits. Low-Q inductors have higher dissipation, resulting Fig.1: a real inductor does not just have pure inductance; it also has parasitic series resistance (Rl) and parallel capacitance (Cp). 30 Silicon Chip in wideband performance. It can be expressed as: Q = 2π × (Epk ÷ Edis) Where Epk is the peak energy stored in the inductor and Edis is the energy dissipated during each cycle. Let’s consider two passive components, an inductor and a capacitor. The reactance of the inductor is Xl = +jωL. Here, j = √-1, Xl is in ohms and ω = 2πf (f is the frequency). For example, a 10µH coil at 10MHz will have a reactance of +j628W. A capacitor has a reactance of the opposite polarity, ie, Xc = 1 ÷ −jωC. To resonate at 10MHz, the capacitor needs a reactance of −j628W, which equates to 25.3pF. But inductors and capacitors are not perfect. A practical inductor can be approximated as an ideal inductor with a series resistor. The coil By Charles Kosina winding will also add a small capacitance across the inductor, as shown in Fig.1. The capacitor is also not perfect but generally has a much smaller inherent resistance, so for this calculation, we can assume it is. The inductor’s Q is defined as Q = Xl ÷ Rl and the -3dB bandwidth of such a tuned circuit is BW = f ÷ Q. So, a tuned circuit with a 10µH coil and a Q of 100 would have a -3dB bandwidth of 100kHz at 10MHz. The Q is important if you’re trying to design something like a bandpass or notch filter. In Fig.2, we have a series tuned circuit fed by a variable frequency source with frequency f, voltage VS and source resistance Rs. At resonance, Xl = −Xc; in effect, a short circuit, so the load on the generator is Rs + Rl. By having a generator with source resistance Rs much lower than Rl, the Fig.2: we can calculate an unknown inductor’s Q (quality factor) using this circuit. It is connected in a series-tuned circuit with a capacitance, and that circuit is excited by a sinewave from a signal generator via a known source resistance. Measuring the input and output AC voltages and calculating their ratios allows us to compute the inductor Q, assuming the Q of the capacitance is high. Australia's electronics magazine siliconchip.com.au voltage measured at Vin will be close enough to VS. The current through the circuit will be Is = VS ÷ Rl. Therefore the voltage at the junction of the inductor and capacitor is Vout = Xl × Is. By measuring Vin and Vout, the Q can be calculated as Ql = Vout ÷ Vin. That assumes that the capacitance has been adjusted to achieve peak resonance with the inductance, ie, Xl = −Xc. That can be done by sweeping the capacitance until the peak Vout voltage is reached. The first design challenge is to have an extremely low generator source resistance. If we have a 10µH coil with a Q of 100, at 5MHz, the effective Rl is 3.14W (314W ÷ 100). If our source resistance is 0.1W, that will give an error of about 1%. But at 1MHz, Rl becomes 0.628W, and this error blows out to 15%. So using a higher frequency will generally result in a more accurate Q measurement. Low source resistance Boonton solved the source resistance problem by having the generator heat a thermocouple using a wire with a very low resistance, as shown in Fig.3. The voltage generated by this thermocouple was measured by a DC meter which indicated how much current was applied to a 0.02W resistor in series with the external inductor. I have a Meguro MQ-160 Q Meter, essentially a 1968 version of the original Boonton 260-A design, using such a thermocouple and resistor. No transistors in this one; it’s all valves! But for our design, a thermocouple is not practical. The HP design eliminated the thermocouple and instead used a step-down transformer. The transformer is fed by a low impedance source, as shown in Fig.4. If our source resistance is 50W, like siliconchip.com.au the output of a typical signal generator, and the turns ratio is 50:1, the effective source resistance is 0.02W (50W ÷ 502), exactly what we want. Unfortunately, it is not so simple as it implies a perfect transformer. Losses in the transformer core plus winding resistance conspire against us and push up the source resistance value. We can improve this by feeding the transformer’s primary from the output of an op amp, which has an impedance close to zero. In this case, a turns ratio of 10:1 is adequate as the resultant 100:1 impedance ratio will give an acceptable load to the op amp. This is what I have used in my design. The transformer is a ferrite toroid of 12mm outside diameter. The primary is 10 turns of enamelled wire, while the ‘one turn’ secondary is a 12mm-long tapped brass spacer through the centre of the toroid. The effective RF resistance of this spacer is extremely low, and the source resistance is then mainly a function of the ferrite material and the primary winding resistance. Table 1 – frequency versus signal source impedance/spacer Frequency Brass Steel 0.1-1MHz ~0.00W 0.02W 2MHz not tested 0.016W 5MHz 0.03W 0.13W 10MHz 0.07W 0.20W 15MHz 0.09W not tested 20MHz 0.15W 0.22W 25MHz 0.10W 0.17W The full circuit of my Q Meter is shown in Fig.5. We require a signal generator with an output of about 0dBm (1mW into 50W or 225mV RMS). You can use just about any RF signal generator. There didn’t seem to be much point in building the generator into the Q Meter since, if you’re building a Q Meter, you likely already have an RF signal generator. I’m using my AM/FM DDS Signal Generator that was described in the May 2022 issue (siliconchip.au/Article/15306). The generator feeds a sinewave into CON1, which is boosted by op amp IC2a. This is a critical item in the design, as it needs a high gain bandwidth (GBW) and slew rate, as well as the capability to drive a low impedance. The Texas Instruments OPA2677 has a GBW of 200MHz, a slew rate of 1800V/µs and can drive a 25W load, which gives us enough output voltage swing up to 25MHz. The toroidal transformer core is a critical part of the design. I tested a Fair-rite 5943000301 core which is readily available from several suppliers. I wound it with 10 turns of 0.3mm diameter enamelled copper wire. A heavier gauge (up to about 0.4mm) may be slightly better, but there has to be enough room in the centre for the spacer to pass through. I then calculated the source impedance by measuring the no-load output voltage followed by a 1W load. I did this for several frequencies, and the results are shown in Table 1. Below 1MHz, there was no measurable difference between no load and a 1W load, so the source impedance must be well below 0.01W. Core losses likely account for the higher source resistance as frequency increases, but the results are quite adequate. Brass spacers are recommended (and will be supplied in kits) due to their superior performance here, at least for the one through the toroid. Fig.3: one method of measuring Q involves current sensing via monitoring the temperature of resistance wire. It has the advantage of keeping the source impedance low, and no complicated shunt sensing circuitry is required. Fig.4: we need an RF signal source with an extremely low but known source resistance for our Q Meter. Since that is difficult to achieve by itself, feeding the signal through a low-loss stepdown transformer greatly reduces the actual source impedance, as seen by the load. Circuit description Australia's electronics magazine January 2023  31 Fig.5: eight relays switch capacitors in parallel to vary the resonant circuit capacitance from around 40pF (the stray capacitance) to 295pF. The signal from the RF generator is amplified by op amp IC2a and fed through step-down transformer T1 to the resonant circuit. The input signal level is monitored via precision rectifier IC2b while the output signal is rectified using D3 and amplified by IC3a. 32 Silicon Chip Australia's electronics magazine siliconchip.com.au The DC output of op amp IC2a is zero or very close to zero, so why do we need a 10µF capacitor in series with the transformer? As the DC resistance of the primary is a fraction of an ohm, the slightest offset voltage in the op amp output could send a high direct current through the toroidal transformer primary and overload the output. That possibility is eliminated with AC coupling. The tuning capacitor is another essential part. My Meguro has a 22-480pF variable capacitor, typical of the tuning capacitors used in valve radios. They are available on sites like eBay, but they are very large and expensive. The only easy-to-get variable capacitor is the sort with a plastic dielectric for AM radios. But once you get above the broadcast band, they are very lossy, with a poor Q, and entirely unsuitable. So instead, I designed a ‘digital capacitor’ with eight relays switching in capacitors with values in a binary sequence of 1, 2, 4, …..128pF. As these are not standard values, some are made up of two capacitors in parallel. For example, 32pF is 22pF in parallel with 10pF. Combining these allows the capacitance to be adjusted in 1pF steps from 0pF to 255pF. The measured stray capacitance due to the tracks, relays etc amounts to 40pF, so the tuning range is 40-295pF. My LC meter shows that it tracks reasonably accurately. All capacitors are not created equal, so I have used somewhat expensive high-Q RF capacitors, available from element14, Mouser, Digi-Key etc. Not all these capacitors have a close tolerance; some are ±2%, which detracts from the accuracy. So it isn’t a ‘real’ variable capacitor but it has the advantage of not needing a calibrated dial and a slow-motion vernier adjustment. Rather than measuring the very low voltage on the secondary side of the transformer, it is more practical to measure the primary side, and for the Q calculation, divide this by 10. I verified this assumption by checking that the voltage ratio corresponded to the turns ratio within measurement accuracy from 100kHz to 25MHz. A precision half-wave rectifier is formed using op amp IC2b in the classic configuration. By placing the rectifier diodes in the negative feedback network of the op amp, their forward siliconchip.com.au Australia's electronics magazine January 2023  33 rectifier feeding a high-­ impedance (10MW/1.5MW) voltage divider. The voltage drop in the diode only introduces a small error in the measurement. The voltage at the junction of this divider is buffered and amplified by IC3a, a TSV912 op amp with an extremely high input impedance – the input bias current is typically 1pA. Switch S1 changes the gain of this op amp for the low and high Q ranges, with the low range giving 8.3 times gain for Q values of up to 100. On the high range, the gain of this stage drops to 1.7 times. Power supply & control Fig.6: the PCB uses mostly SMD components for compactness, although none are particularly small. The orientations of the following components are important: all relays, ICs and diodes, plus the Arduino Nano. ZD1, IC4, CON3 and associated parts form the optional debugging interface. voltages are effectively divided by the (very high) open-loop gain of the op amp. On positive excursions of the output pin of IC2b, the 330nF capacitor at TP3 is charged up through diode D1. The extra diode, D2, is needed as without it, negative excursions would saturate the op amp and lead to slow recovery, limiting its frequency range. Both diodes are 1N5711 types for fast switching. 34 Silicon Chip The output of IC2b is amplified by IC3b, and the resulting filtered DC voltage at TP4 is about 1.9V. The secondary voltage of the transformer is typically 200mV peak-topeak or about 70mV RMS. With a Q of 100, the voltage output at the junction of the inductor and tuning capacitor would be 20V peak-to-peak or 7V RMS. That is not a suitable voltage to apply to the input of an op amp! So I used schottky diode D3 as a half-wave Australia's electronics magazine A MAX660 switched capacitor voltage inverter (IC1) provides a nominally −5V supply to the OPA2677 (IC2). This is needed for proper operation of the half-wave precision rectifier, IC2b, as the voltage at its input can swing below ground. The MAX660 is not a perfect voltage inverter, and with the current drain of the OPA2677, its output is about −3.6V, but that is adequate. The rest of the circuit operates from a regulated +5V DC fed in externally, eg, from a USB supply. An Arduino Nano module is used as the controller. This is a readily-­ available part from many suppliers at a reasonable price. Two analog inputs are used for measuring the voltages, eight digital outputs switch relays, the two I2C serial lines drive the OLED, and there are inputs for the control rotary encoder and LOW/HIGH switch sensing. The rotary encoder (EN1) is used to adjust the ‘digital capacitor’ value; its integral pushbutton switch toggles between steps of 1pF and 10pF. As usual with my designs, I have added a simplified RS-232 interface using hex schmitt-trigger inverter IC4 to aid code debugging. IC4, ZD1 and the two associated resistors can be left out unless you want to use the debugging interface. Eight 2N7002 N-channel Mosfets (Q1-Q8) drive the relay coils, while eight diodes across the relay coils (D6D13) suppress switching transients. The resonant frequency tuning is done by selecting an appropriate frequency from the external signal generator and adjusting the variable capacitance value. Ideally, the peaking should be done with an analog meter, siliconchip.com.au but I have provided an onboard LED, LED1, the brightness of which depends on the Vout voltage. It’s simple enough to adjust the capacitance to achieve maximum brightness. The third line of the OLED also shows the output voltage of IC3a, which can be used to accurately achieve resonance too. Connector CON5 drives an optional external 0-5V moving coil meter. You can add such a meter if a larger-­thanspecified enclosure is used to house the PCB. The power supply is a standard 5V USB charger. I have not included reverse polarity protection, but an offboard 1A schottky diode (eg, 1N5819) could be added in series if desired. (0.3in) pitch, then the rotary encoder, switch and LED. Use a 5mm plastic spacer for the LED, so it is flush with the back of the front panel. Wind ten turns of the specified enamelled copper wire onto the toroidal core, taking care that the turns are equally spaced around the circumference, to the extent possible, and the ends line up with the two pads marked PRIM on the PCB. Carefully attach the toroid so that it is centred on the mounting hole. Attaching the spacer to the board makes that easier. It may be anchored in place by an insulated wire across the two pads on the opposite side. It is not a shorted turn as only one side of this wire is connected to the ground plane. I recommend fitting socket strips for mounting the Arduino Nano module as they make replacing a faulty module easy (I have blown up a couple in the past!). The OLED screen also plugs into a 4-pin socket strip and is held in place by two 15mm-long M2 or M2.5 Construction The construction uses two PCBs (see Figs.6 & 7). The main one has all the electronics while the other has the screw terminals for the DUT and external capacitor. It is also used as a front panel and has a rectangular cutout for the OLED, holes for the controls and lettering. It is designed to fit in a RITEC 125 × 85 × 55mm enclosure, sold by Altronics as H0324. The top board/front panel is 98 × 76mm and fits snugly into the recess in the clear lid of the enclosure. This board could be used as a template for accurately drilling the holes in the clear lid. But other enclosures may be used as long as they have the same or slightly greater dimensions as the H0324. For those wishing to add the 0-5V moving coil meter, this requires an additional width of 45mm. A suitable 158 × 90 × 60mm enclosure is available from AliExpress suppliers at a reasonable price, but be aware that delivery can take quite a few weeks. Most components on the PCB are surface-mount types, but there are no fine-pitch ones, which simplifies construction. Solder the four SOIC chips first, then all the passives, which are mostly M2012/0805 size (2.0 × 1.2mm). The relays take a bit of care to ensure they are square on the board so that it looks neat. On the opposite side of the board are eight 1N4148 equivalent diodes; ensure they are installed with the correct polarity, with the cathode stripes to the side marked “K”. After the SMDs, add the throughhole diodes, which have a 7.6mm siliconchip.com.au Only the Arduino Nano, headers and eight diodes are on the underside of the Q Meter PCB. Note how the windings for T1 are spaced evenly around it. Australia's electronics magazine January 2023  35 Almost all the parts mount on the main PCB. The only chassismounting components are the DC input socket and optional power switch. screws through 8mm untapped spacers. Carefully slide off the plastic strip on the four pins of the OLED so that it sits lower. The board must be thoroughly cleaned with circuit board cleaner. There are high impedances throughout the circuit, and leakage through flux residue would affect its operation. So you must remove that residue. Testing Once the board has been fully assembled, cleaned and inspected, but before it is mounted in the case, attach the four 12mm spacers but not the front panel board, and connect the 5V supply. The OLED should show an initial message with the firmware version number. Using a coax cable, feed in a sinewave from a signal generator at about 1MHz. An oscilloscope probe on TP1 should show a clean sinewave, with an output of about 2V peak-to-peak. If the output of the signal generator is too high, you will get flattening on the negative half cycle. In that case, back off the level for a clean sinewave. Transfer the ‘scope probe to the top of the spacer that passes through the toroid, and the voltage should be onetenth of that measured at TP1. Measure TP4 using a DC voltmeter; you should get a reading of about 2V. Note that these values will depend on the output of the signal generator and could vary. Rotate the encoder and note that the capacitance value varies by 1pF per detent. Depending on the encoder, it might go backwards. If so, plug a 36 Silicon Chip jumper on the Arduino Nano’s programming header between pins 4 and 6; that will correct the direction. Push down the knob to change the resolution, and the capacitance should then change by 10pF per detent. By winding it fully clockwise, the maximum indicated capacitance should show as 295pF on the bottom line of the OLED, with the minimum being 40pF. Connect a 10µH moulded inductor between the two “L” spacers, using 3mm machine screws to hold it in place. Adjust the capacitance to 100pF, switch to LOW Q mode and adjust the signal generator frequency to about 5.5MHz. The LED should light up; tune the capacitance for maximum brightness. The second line of the OLED will then most likely display “TOO HIGH”. Switch to HIGH Q mode, which will dim the LED, and re-tune for maximum brightness. Depending on the inductor, a typical Q reading will be about 120. If you get a sensible reading and can peak the LED brightness by varying the capacitance, your Q Meter is most likely functioning correctly, so it can be finished. The front panel is mounted on the front of the case, and the main PCB may now be attached by the four spacers using four 8mm M3 machine screws. To improve the appearance, use black screws or spray the heads flat black. Note that the binding posts must make electrical contact with the bare pads on the front panel PCB; attach them with the supplied nuts and make sure they are making good contact. The tapped spacers connecting the two boards must also make good electrical contact at both ends. Using it The operation of the Q meter requires some initial measurements and calculations. We need to know at least the approximate inductance of the DUT. I use my LC Meter for measuring this, as described in the Fig.7: the circuitry on the front panel PCB just consists of one large track connecting the two red terminals and smaller tracks connecting the upper screws to their adjacent binding posts. It also has holes and labels for the controls and screen. Australia's electronics magazine siliconchip.com.au November 2022 issue of Silicon Chip (siliconchip.com.au/Article/15543). With the inductance known or guessed, we need to determine the frequency at which to measure the Q. That will be influenced by the inductor value and the frequency at which you want to use the inductor. Once you’ve selected a frequency, plug the values into the formula: Parts List – Q Meter Accuracy 1 RF signal generator (see May 2022; siliconchip.au/Article/15306) ● 1 RITEC 125 × 85 × 55mm plastic enclosure [Altronics H0324] ● 1 double-sided PCB coded CSE220806B, 99 × 79mm 1 double-sided PCB coded CSE220807A, 98 × 76mm, black solder mask 1 chassis-mounting SPST toggle switch with solder tabs (S1) 1 0-5V analog meter (optional) ● 1 Arduino Nano (MOD1) 1 0.96in OLED display module with I2C interface and SSD1306 controller (MOD2) [Silicon Chip SC6176 (cyan)] 8 G6K-2F-Y SPDT SMD relays (RLY1-RLY8) 1 rotary encoder with integral pushbutton (EN1) 1 knob to suit EN1 1 Fair-rite 5943000301 ferrite toroidal core, 12mm OD, 8mm ID, 5mm thick (T1) 1 30cm length of 0.25-0.4mm diameter enamelled copper wire (T1) 1 SMA edge connector (CON1) 2 2-pin polarised headers (CON2, CON5) 1 3-pin polarised header (CON3) ● ♦ 1 2.1mm or 2.5mm inner diameter chassis-mount jack socket (CON4) ● 2 red 4mm chassis-mounting banana socket/binding posts 2 black 4mm chassis-mounting banana socket/binding posts 4 M3 × 12mm brass spacers 4 M3 × 5mm nickel-plated panhead machine screws 4 M3 × 8mm nickel-plated panhead machine screws 2 M2 × 16mm machine screws and nuts 2 8mm-long untapped plastic spacers 1 5mm-long plastic LED spacer 1 20cm length of light-duty figure-8 hookup wire ● Semiconductors 1 MAX660M switched capacitor voltage inverter, SOIC-8 (IC1) 1 OPA2677 dual ultra-high GBW op amp, SOIC-8 (IC2) 1 TSV912 dual high input impedance op amp, SOIC-8 (IC3) 1 74HC14 hex inverter, SOIC-14 (IC4) ♦ 1 3mm red diffused lens LED (LED1) 8 2N7002 Mosfets, SOT-23 (Q1-Q8) 1 4.7V 400mW axial zener diode (ZD1) ● ♦ 3 1N5711 axial schottky diodes (D1-D3) 8 LL4148 75V 200mA diodes, SOD-80 (D6-D13) This meter is certainly not as accurate as the HP4342-A meter mentioned earlier. Without any standard coils of known Q, it is difficult to determine the true accuracy. But even the HP4342-A does not claim any better accuracy than ±7% for frequencies below 30MHz, and considerably worse for higher frequencies (see the PDF at siliconchip.au/link/abgn). I compared my results with the Meguro meter, but being over 50 years old, it is hardly to be trusted! Still, measurements of the same coil with the Meguro and my meter were genSC erally within 10%. Capacitors (all SMD M2012/0805 X5R or X7R) 3 10μF 16V 3 330nF 50V 10 100nF 50V RF capacitors (all ±2% 200V SMD M2012 or M1608 C0G/NP0 unless noted) 2 100pF 50V 1 10pF 1 56pF 2 8.2pF 1 27pF 1 3.9pF ±0.1pF 1 22pF 1 2.2pF ±0.1pF 1 15pF 2 1.0pF ±0.1pF Resistors (all SMD M2012/0805 1%) 1 10MW 3 3.3kW 1 1.5MW 1 1.2kW 1 12kW 1 1kW 3 18kW 1 270W 3 10kW 1 51W 4 4.7kW C = 25330 ÷ (2 × f × L) Where C is in pF, f is in MHz and L is in µH. If you get a value of C below 40pF, select a lower frequency and redo the calculation; if you get a value above 295pF, choose a higher frequency. Repeat until your calculated capacitance is in the range of 40-295pF. Set the capacitance to that value and adjust the frequency from the signal generator, or the capacitance, for resonance. The resulting Q will be shown on the second line of the OLED. If the switch is set to LOW and the Q exceeds 100, the second line will show “TOO HIGH”. In that case, switch to the HIGH position. I find that it is better to start with the switch set to LOW as it is easier to figure out if you are close to resonance. The “C” terminals allow a capacitor to be placed in parallel with the internal capacitance in case you can’t achieve resonance at a sensible frequency with the available range. So that it doesn’t detract from the Q, it should be a high-quality RF capacitor. ♦ optional components only required for debugging interface KIT (SC6585) – $100 + P&P: includes everything in the parts list that isn’t marked with a ● PCBs are also available separately siliconchip.com.au ● Kit – a kit is available with all the above parts except those marked with a red circle. Its catalog code is SC6585 and it costs $100 + P&P ($90 + P&P for active subscribers). Note that the Arduino Nano is supplied unprogrammed. The PCBs are also available separately. Australia's electronics magazine January 2023  37