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This unique project demonstrates what can be achieved with a relatively simple circuit and some clever programming. With only a microcontroller and a handful of components, it functions as a wide-ranging, multi-frequency inductance and Q-factor meter. Inductance & Q-Factor Meter Pt.1: By LEONID LERNER I NDUCTORS ARE UBIQUITOUS, being indispensable in circuits such as loudspeaker crossover networks, switchmode power supplies and RF amplifiers. Unlike other components, inductors are often handmade, particularly when prototyping or assembling a do-it-yourself project. At a minimum, this suggests the need for a meter to check inductance values prior to use in circuit. But that is not the end of the story. Of all the passive components, inductors typically show the greatest deviation from ideal behaviour. This is due primarily to coil resistance and the hysteresis of the core material. The picture is further complicated 64  Silicon Chip by the fact that the losses are frequency dependent. The skin effect in copper wire and the complicated frequency characteristics of magnetic materials both come into play and are apparent even at audio frequencies. To provide a more informative picture of inductor performance then, this new meter allows you to measure the Q factor of a prospective resonant circuit at the operating frequency. If you’ve never heard of Q factor, then read on . . . Measuring L & Q There are several basic methods of measuring the inductance (L) and the Q-factor of a tuned circuit, the most common being “temporal” (time domain) and “spectral” (frequency domain). The spectral method was described in the “Poor Man’s Q-Meter” article in the July 2004 issue of SILICON CHIP. It consists of applying a sinusoidal voltage of varying frequency to a resonant circuit and measuring the circuit response as a function of applied frequency. The response of such a circuit will generally follow that shown in Fig.1, with a peak at a given frequency, dropping away on both sides in a bell-shaped curve. Circuit theory demonstrates that the peak angular frequency squared is just the inverse of the inductance (L) times the capacisiliconchip.com.au Specifications Range Inductance: 200nH - 999μH Q-Factor: 1-120 (approx.) Power Supply 9V DC 300mA plugpack Features (1) Internal or external tank capacitance facility for accurate Q measurements (2) Measurement frequency autoranging up to 20MHz tance (C). So if we know C, inductance can be found. On the other hand, the Q factor is the ratio of the peak frequency to the width of the bell-shaped curve at half-power. This is how the Q is manifest experimentally. Theoretically, it is defined as the ratio of the circuit reactance to its resistance at resonance. It should be emphasised that the preceding definitions are only approximations but give excellent results provided Q is greater than 2 or so. For heavily damped resonant circuits, the relationships between waveform and circuit parameters are more complicated. However, we are not interested in such circuits here. Fig.1: the spectral response of a resonant circuit reveals a peak at a given frequency, dropping away on both sides in a bell-shaped curve. The Q factor is manifest as the ratio of the peak frequency to the width of the bell-shaped curve at half-power. Temporal method The temporal method of inductance measurement is adopted in this design. It is based on the fact that when a rectangular pulse is applied to a resonant LCR circuit, such as that shown in Fig.2, decaying oscillations give rise to a ringing waveform. These oscillations continue until all energy is dissipated in the circuit resistance, with their frequency the same as that at which the peak occurred in the spectral response. The Q factor in the temporal response manifests itself as the ratio of the oscillation coefficient (the angular frequency) to twice the decay coefficient. We can use this information to measure the L and Q of a parallelresonant circuit with a square wave generator and a scope. The generator is connected to the tuned circuit through a large resistor, so as not to appreciably load the circuit and thereby alter the Q. This resistance should be larger than the series resistance multiplied by Q2. siliconchip.com.au Fig.2: the temporal method used in this design relies on decaying oscillations after a rectangular pulse is applied to the resonant circuit. The Q factor manifests as the ratio of the oscillation coefficient (the angular frequency) to twice the decay coefficient. A typical oscilloscope trace of a ringing waveform set up in a resonant circuit by such a generator is shown in Fig.3. The period is the time required for the signal to undergo N oscillations, divided by N. The Q factor is the number of oscillations required for the peak amplitude (starting at some convenient peak) to drop to about 0.043 of its initial value. In practice, one can get better accuracy by counting the number of oscillations for the amplitude to drop to one fifth, and multiplying this number by two. The above procedure is the basis for this project, with an AT90S2313 microcontroller performing the multiple functions of generator, scope and calculator. A liquid crystal display (LCD) and keypad are also included to provide a convenient means of setting basic parameters and observing the measurement results. Fourier transformed It is interesting that one can get from the ringing waveform of the temporal response to the bell-shaped curve of the spectral response by a technique called the Fourier Transform, or its numerically useful form, the Fast Fourier Transform (FFT). This means one February 2005  65 Fig.3: this scope shot shows the response of an LCR circuit to an applied pulse. Decaying oscillations give rise to a ringing waveform, which continues until all energy supplied by the pulse is dissipated in the circuit resistance. The frequency of oscillation is the same as would occur at the peak in the spectral response. does not actually have to make spectral measurements in order to obtain the spectral response. This is useful because it is much easier to extract the parameters of interest from the spectral plot than from the temporal plot. The former involves just finding a peak in the data, while the latter requires establishing and then counting the zero-crossings. Another advantage in using FFTs is that the effects of the inevitable analog noise, as well digitising distortions, are minimised, as they are separated from the signal in the Fourier analysis. Depending on circuit Q, our meter can measure inductances as low as 200nH and as high as 10mH. The range of Q measured varies from about 1 to 120. Circuit basics Before looking at circuit operation in some detail, it is instructive to consider the block diagram in Fig.4. The central component of the system is an Atmel AT90S2313 microcontroller. This particular micro was chosen because it is relatively cheap yet includes all of the features needed to minimise the total component count. The micro controls a “pulser”, which is used to excite a tank circuit. The tank circuit consists of the in- ductor under test and a paralleled capacitor. The capacitor can be selected by the user and connected externally. Alternatively, one of three internal capacitor values can be chosen from the keypad. To minimise loading and compensate for circuit losses, the waveform from the tank circuit is buffered and amplified by an op amp. Following this, it is fed into a sample-and-hold (S/H) circuit and then into an analogto-digital converter (ADC). The ADC functions are contained mostly within the micro so they do not appear on the diagram. A ramp converter was chosen for its simplicity and low cost. For readers not already familiar with this type of converter, its operation can be summarised as follows: A conversion cycle begins with the charging of a capacitor from a constant-current source. As the capacitor begins to charge, a binary counter starts counting from zero. The increasing capacitor voltage (the “ramp”) is Fig.5 (right): complete circuit diagram (minus power supply) for the meter. A high-speed sample and hold circuit made up of a simple counter (IC2), analog switch (IC3) and some clever programming allows the meter to measure resonant circuits at frequencies up to 20MHz. Fig.4: the AT90S2313 microcontroller forms the heart of this design. After stimulating the tank circuit, it digitises the resulting waveform and displays the results on an LCD. 66  Silicon Chip siliconchip.com.au siliconchip.com.au February 2005  67 ing port bits PD3 and PD4 (IC5, pins 7 & 8). Signals from these pins are fed through isolating diodes D6 and D7 to current amplifiers Q3 and Q6 and from there to switching transistors Q4/ Q5 and Q7/Q8. Two medium-current transistors are used in parallel to reduce the dynamic collector-emitter resistance and hence its influence on the circuit Q. Even so, the transistors contribute about 0.5W series resistance and the influence of this on the Q should be borne in mind. Relays could have been used to reduce the series resistance further. However, these are slow, prone to failure and not really in accord with our solid-state approach. In addition, the use of high-current audio transistors is precluded by their high output capacitance. If there is some concern about the contribution of the internal circuitry to the Q factor then you can leave out the link and use an external tank capacitor. This is the view inside the completed prototype. The full construction details will be published in Pt.2, next month. continually compared with the input voltage. When the two voltages are equal, the comparator stops the counter, whose count is then proportional to the input voltage. Although simple, ramp converters have a comparatively long conversion time and a somewhat reduced precision. In this application, precision is not of particular concern since it is the time characteristics of the signal that are of paramount importance. However, conversion time is important. Inductors in the order of a few hundred nanohenries require measurement frequencies of tens of megahertz to achieve a sufficiently large Q and so an accurate measurement. This is clearly well beyond the capabilities of our simple ramp converter. Even if the design was to use a dedicated high-speed (20MHz or better) ADC, the micro would not be fast enough to store the results of each conversion. All this overlooks the fact that the ringing waveform is repetitive. It can therefore be digitised at low speed by repeatedly stimulating the tank circuit and measuring each waveform at progressively larger offsets from time zero. 68  Silicon Chip To achieve the desired 20MHz sampling rate, measurements must be made at 25ns intervals. This is achieved with the aid of a programmable sample-and-hold block which holds each measurement long enough for the low-speed ramp converter to complete its task. Detailed operation The circuit diagram for the majority of the L/Q Meter appears in Fig.5. Let’s start at the test terminals, where the inductor under test and capacitor(s) are connected to form the tank circuit. Transistor Q1 is used to pulse the tank circuit. It is driven via a 100W current limiting resistor from output port bit PD5 (IC5, pin 9). A second 100W resistor in the emitter circuit limits peak pulse current to about 50mA. Diode D2 provides isolation between the tank circuit and the driver so as not to dampen the oscillations. Installing a shorting link between the “A” and “B” terminals links the inductor under test with an internal set of capacitors. A 1nF capacitor across the terminals fixes the minimum capacitance. Two other capacitor values (10nF and 100nF) can be switched into the circuit under program control us- Fast op amp needed So as not to load the tank circuit, the output signal is buffered by an op amp (IC4), which is connected in a non-inverting configuration for high input impedance. An AD8055 op amp was chosen for the task as it has high gain-bandwidth product and high slew rate and is stable when driving capacitive loads at low gains. Lower spec op amps are not suitable here, as they would severely limit the frequency range of the meter. Ideally, the output from the op amp should swing between about 0-4V maximum, which is the maximum input range of the comparator. To this end, op amp gain is set to about 1.8 by the 1.2kW and 1kW resistors, counteracting losses in the circuit. To maximise dynamic range and minimise the influence of noise and digitisation errors, the AD8055 and analog switch (IC3) are powered from ±5V supplies. Furthermore, the inverting input of the op amp is biased at -1.8V, meaning that the output (pin 6) will swing either side of +1.8V. This scheme makes the most of available headroom, which is limited to about 3.7V. Note that the micro is programmed to reject the initial part of the ringing should saturation occur. Hold it a moment The output of the op amp drives a siliconchip.com.au Fig.6: the power supply section. A conventional +5V regulator (REG2) powers the entire circuit, while a switchmode inverter (IC6) generates -5V for some of the analog circuitry. An LM337 negative regulator (REG3) is used only to generate a bias voltage for op amp IC4. high-speed sample-and-hold circuit ahead of the comparator (ADC) input on pin 12 of the microcontroller. The S/H circuit consists primarily of an analog switch (IC3c) and 680pF storage capacitor. As mentioned earlier, the micro digitises a measurement by repetitively sampling successive waveforms. Samples are taken at incremental offsets from time zero to build a complete and accurate digitisation of the ringing waveform. Sampling begins by closing the analog switch (IC3c) at time zero. After the programmed delay, the switch is opened, leaving the 680pF storage capacitor charged to the waveform voltage at that instant. Our slow ADC then has sufficient time to digitise the voltage, after which it is stored and the cycle repeats. This is represented graphically in the scope shots of Figs.7(a)-7(d). Unfortunately, the 100ns cycle time of the micro means that it is too slow to directly control the analog switch (IC3c). With a maximum 20MHz sampling rate, we need 25ns resolution. This is provided by external logic, consisting of a 40MHz oscillator module (OSC1), timing circuits (IC1 & IC2) and a level converter (Q2, D1, IC3d, siliconchip.com.au etc), all under control of the Atmel microcontroller (IC5). Level conversion Let’s look at the level converter circuit first. It consists mainly of transistor Q2, diode D1 and analog switch IC3d. The sole purpose of this circuit is to convert the 0-5V levels from the NAND gate output (IC1a) to ±5V levels to control the S/H switch (IC3c). Since the minimum sample time is only 25ns, Q2 is required to switch in nanoseconds and have a slew rate in the order of 1000V/ms. This is achieved with the use of a high beta transistor and 100W resistors in the base-emitter circuits, as well as the germanium diode (D1) between the collector and base. The results can be seen in the oscilloscope trace of Fig.7(a). Q2 inverts the control signal from IC1a, so a spare analog switch (IC3d) is used to invert it again before it is fed to the control pin of the S/H switch. Timing secrets The two divide-by-2 sections of a dual decade counter (IC2) are cascaded to divide the 40MHz clock down to 10MHz for the micro’s clock input on pin 5. The divide-by-5 section of the second half of the decade counter (IC2b) is used to derive two out-ofphase 8MHz timing signals. Output 3 (bit 2) of the counter (pin 9) is used by the micro as an 8MHz synchronisation signal. It is high during only one state of the five states of the counter, allowing precise determination of the instantaneous state of the 8MHz clock with respect to the 10MHz clock. Output 2 (bit 1) of the counter is NANDed with port bit PD0 (pin 2) of the micro via IC1a to generate the “hold” signal for the S/H circuit. As the micro’s port outputs are synchronised to its 10MHz clock, the difference between the rising edges of the two signals on IC1a’s inputs allows generation of 0ns, 25ns, 50ns and 75ns delays under program control. This can be seen in the simplified timing diagram of Fig.8. Output 2 is also NANDed with port bit PD1 via IC1d so that the micro can freeze the counter. Note that Output 2 is used here instead of Output 1 as it goes high earlier in the counting cycle, thus allowing for the propagation delay through gates IC1c-IC1d and IC2b. Digitising The micro program performs analog February 2005  69 How The Ringing Waveform Is Digitised Fig.7(a): the following series of scope shots were captured at progressively longer timebase settings and provide an insight into how the ringing waveform is digitised. Here, the green trace shows the waveform at the S/H output (pin 9 of IC3c), while the red trace shows the control signal on pin 6. Note the very fast transitions of the latter, which for the all-important trailing edge (hold) constitutes 7ns, or 1400V/ms. The waveform is oscillating at a 1.8MHz rate and its instantaneous value is captured when the control signal goes low. Also, note that the voltage at the S/H output doesn’t decay noticeably during the hold period (red trace low), when the analog to digital conversion takes place. Fig.7(c): with a timebase of 200ms/div, the sample-and-hold control signal is now just a succession of spikes and is not shown. At this time scale, the sequence of flat plateaus reproduces a digitised version of the original ringing waveform of Fig.7(a), occurring at a rate almost 1000 times faster. to digital conversions by using the AT90S2313’s internal comparator in a ramp converter. This requires a voltage rising at a constant rate to be produced at the inverting input of 70  Silicon Chip Fig.7(b): a waveform is acquired by continuously stepping the delay between the pulse applied to the tank circuit and the hold signal. The rising plateaus generated by successively greater delays capture the rising edge of a particular sinusoidal cycle and show how a repetitive 1.8MHz signal is effectively frozen and reproduced on a much larger time scale. Note that the hold period or the time interval between successive pulses, reflected in the length of the plateaus, increases with increasing voltage. This is because the conversion time of the ramp converter is proportional to the sampled voltage. Fig.7(d): this final shot is at the longest timebase setting (2ms/div). Each bunch of oscillations is the digitised ringing waveform in the previous figure. Between acquisitions the micro performs calculations, so the S/H circuit is idle and the charge on the 680pF capacitor decays. comparator IC5 (pin 13). This is produced by an LM334 constant current source (REG1) which is used to charge a 4.7nF capacitor. The LM334 provides temperature compensation in this time-critical part of the circuit. The input signal (via the S/H circuit) is applied to the non-inverting input of the comparator (pin 12). The output siliconchip.com.au New VAF speakers not just for audio perfectionists VAF Speakers have a legendary reputation for providing the best accuracy and value. Fig.8: the time difference between the rising edges of 8MHz and 10MHz clock signals are exploited to enable high-speed sampling. The micro latches a high on PD1 (pin 3) on the rising edge of its 10MHz clock and after a 0, 25, 50 or 75ns delay, the rising edge of the 8MHz clock freezes the input voltage at that instant. of the comparator is programmed to trigger a counter interrupt inside the AT90S2313 when the ramp voltage exceeds the input voltage. Note that the LM334 is rather slow compared to the speed of the rest of the circuit, so current is not switched at its input terminal. Instead, switching is performed at pin 13 of the micro, which is connected to an internal pulldown transistor. This shunts current from the LM334 until the conversion commences. Once enough of the waveform is acquired, the microcontroller performs an FFT of the sample and finds the spectral peak. The FFT is a complicated mathematical procedure and is quite computationally intensive. It is therefore usually performed on highspeed floating-point processors such as Intel’s Pentium class and above. However, speed is not of paramount importance in this application. More importantly, the results must be accurate and this was confirmed by comparing the results of two FFTs, one performed on a Pentium and the other on an AT90S2313. Display and keypad A 2-line x 16-character LCD module, keypad and ISP (in-system programming) interface to the micro via port B (PB2 - PB7) and one bit of port D (PD6). A number of port B lines are shared between devices. The LCD module is interfaced in 4-bit rather than 8-bit mode, so only its upper data lines (DB4 - DB7) are connected. The keypad has 12 keys, organised siliconchip.com.au in a matrix of 4 rows x 3 columns. The micro pulses each row in turn and polls the columns to determine which key is being pressed. Note that 4.7kW resistors are included in series with all the keypad lines to protect the port pins. This means that if a key is pressed while the micro is updating the LCD, no harm is done. Power supply The power supply section of the L/Q Meter appears in Fig.6. Starting at the DC input socket, diode D9 provides reverse polarity protection ahead of a 7805 positive voltage regulator (REG2). This regulator provides +5V for the entire board. As explained earlier, -5V is also needed for op amp IC4 and the analog switch (IC3), and this is generated from the +5V rail by a MAX635 switchmode voltage inverter (IC6). As shown, this device requires only a diode (D8), inductor (L1) and filter capacitor to function as complete switchmode inverter. The -5V rail is reduced to -1.8V by an LM337 negative voltage regulator (REG3). The 120W and 56W resistors between the “GND” and “OUT” terminals set the output voltage to -1.8V, to be used as a bias voltage in the op amp circuit. Next month They are also available as kits because we know that’s the way enthusiasts like them. VAF’s brand new Generation 4 DC-Series is now available and offers extreme levels of accuracy at incredible prices. They go very deep so they can be used for Home Theatre without a subwoofer in many rooms. They are very sensitive so they don’t need big expensive amps to drive them. They can take high power so if you have a huge room or simply want to play loud, you can. They also work well close to walls so you can use them in small rooms too. VAF Speakers are used by the ABC, Parliament House in Canberra, and in preparation of many international DVD titles in Australia.... You can use them too. Buy direct from the people who make them, and for less than you may think. 4 new kits from $449pr to $1,999pr. If you want instant results, fully assembled versions are also available. For Info or to Order FreeCall 1 8 0 0 8 1 8 8 8 2 email vaf<at>vaf.com.au www.vaf.com.au That’s all we have room for this month. Next month, we will give the full construction details and describe how the new Inductance & Q-Factor SC Meter is used. February 2005  71