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Circuit Surgery Regular clinic by Ian Bell Electronically controlled resistance – Part 8 T his month, we conclude our series on electronically controlled resistance with a look at using digipots to control active filter circuits. Like previous articles, we will discuss general circuit design issues and approaches to simulation using LTspice. Filters are a large and complex area of electronics, so we will start with some general background before discussing digipot circuits. Gain Gain Low pass High pass Frequency Gain Frequency Gain Bandpass Bandstop Filter basics A filter is a circuit which passes certain frequencies and rejects others. That is, the gain is designed to be relatively high over a range of wanted frequencies (the passband) and low for frequencies outside this range (the stopband). There are four basic classes of filter, referred to as ‘bandforms’, which are shown in idealised form in Fig.1. These are graphs of the filter’s frequency response – that is, plots of gain versus frequency. Low-pass filters let low frequencies through and block high frequencies. High-pass filters let high frequencies through and block low frequencies. Bandpass filters let a specific range of frequencies through. Bandstop filters reject a specific range of frequencies. There are few other bandforms forms beyond these basic classes. A notch filter is a bandstop filter with a very narrow stopband, which can be useful for rejecting a specific unwanted frequency. A comb filter has multiple, regularly spaced stopbands and passbands. There are also ‘all pass’ filters which have constant gain, but a specific phase shift response with frequency. The idealised (so-called ‘brick wall’) filters in Fig.1 cannot be implemented – it is not possible to have an infinitely fast transition from passband to stopband in a real circuit, so the transition occurs over a range of frequencies. Furthermore, the gain in the passband may not be constant (as it is implied by Fig.1) and the stopband gain will not be either zero (complete rejection) or constant at some low level. Fig.2 shows a low-pass response with various features that occur in real circuits. On filter response plots the gain or attenuation is usually expressed in decibels, which is a logarithmic scale. For voltage 46 Frequency Frequency Fig.1. Basic filter bandforms. gain A the value (in decibels,dB) is given by: 20 × log10(A). The (horizontal) frequency axis of the graph is also usually logarithmic, with the scale marked in multiple-of-ten steps, referred to as ‘decades’. Response types There are various filter response types available named after their related mathematics, such as Butterworth, Bessel and Chebyshev filters. The features shown in Fig.2 vary with different response types and there is a trade-off in terms of desirable features. For example, Butterworth filters have maximally flat passbands with a relatively slow change of gain near the cut-off, while Chebyshev filters have significant passband ripple, but their gain decreases more rapidly near the cut-off. For an ideal filter, the transition from passband to stopband occurs at a single frequency. For real filters the transition from passband to stopband occurs over a range of frequencies so we need to specify exactly what we mean by ‘cut-off frequency’. For a flat passband the cut-off is often defined as the frequency where the filter’s gain is –3dB with respect to the passband gain. This is the point where the output signal has half the power it has in the passband. For filters with ripple, the cut-off frequency is usually defined as the frequency where the response has dropped by an amount equal to the ripple size relative to the maximum passband gain (as seen in Fig.2). Gain/dB Pass band Pass band ripple Passband gain Transition region Roll-off gradient in dB/decade Stop band Stopband gain Stopband ripple Cut-off frequency fc Stopband frequency fS Frequency f (log scale) Fig.2. Features of filter frequency response curves. Practical Electronics | April | 2023 Fig.3. Low-pass response for various Q values. The slope of the frequency response in the transition region/stopband (see Fig.2) indicates how quickly the filter’s gain drops as the frequency moves away from cut-off. For many filters, at frequencies well into the transition region/stopband, the response tends to decrease as a straight line when plotted on a graph of decibels against log frequency. The slope is measured in dB per decade and is called the ‘roll-off’. The roll-off may be different (and changing) near the cut-off, but the term usually refers to ultimate roll-off, at a frequency sufficiently far from the cut-off. The ultimate roll-off is determined by the order of the filter, the higher the order the faster the falloff. A single RC filter is first order and rolls off at 20dB/ decade, while an N-th order filter rolls off at 20 × N dB/decade. The order of the filter determines the ultimate rolloff, but the response type (Butterworth, Chebyshev and so on.) determines the shape of the response near the cut-off. Q – quality factor and bandstop filters are often required in radio circuits. For low-pass filters we typically require relatively low Q values because higher Q values result in a sharp peak around the cut-off frequency (see Fig.3). Usually, we would not want this peak to be very high. The situation is the same for high-pass filters. For these filters the damping factor (ζ =1/ (2Q)) is often used instead of Q as it is perhaps more intuitive However, the reciprocal relationship means they are fundamentally the same thing. Higher damping results in a slower, smoother transition from passband to stopband. The properties of filters are related to resonance – the tendency of some systems to respond at greater amplitude when applied oscillations match the system’s natural frequency of vibration. The peaks seen in Fig.3 occur at the resonant frequency. The resonant frequency is a ‘natural’ property of the filter, or to put it another way, fundamentally related to the mathematics of the filter’s function. The cut-off frequency is effectively arbitrarily defined, so they are not the same thing. The Q, or ‘quality factor’, of a filter determines the response type (shape). Fig.3 shows the response of several second-order low-pass filters with Frequency scaling factor different Q values. The responses are For a particular response type, order the same at frequencies a long way from and definition of cut-off frequency (fc) cut-off (both high and low) but are very there will be a fixed relationship different around the cut-off point. between the resonant frequency (f0) and For bandpass filters, Q is the ratio of cut-off frequency, which can be bandwidth relative to centre frequency. If expressed as a frequency scaling factor Electronically Resistance –(FPart 8 a band-pass filter has aControlled centre frequency s), such that: of f0 and a bandwidth of fb the Q factor 𝑓𝑓! = 𝐹𝐹" 𝑓𝑓# is given by Q = f /f . High-Q bandpass 0 b Practical Electronics | April | 2023 𝐴𝐴 = 1 + 𝑅𝑅$ 𝑅𝑅% The scaling factors are typically, but not always, in the range 0.2 to 2. For Butterworth filters with the cut-off defined as –3dB, the frequency scaling factor is 1. We have discussed frequency response in detail, but filters are also characterised in terms of their phase response (how phase shift varies with frequency). Phase shift is a measure of delay relative to the cycle time at the frequency of interest and ideally increases linearly with frequency – this implies that the absolute delay time is equal at all frequencies. Different filter types have different phase responses. As well as the variation of gain and phase with frequency, the time-domain response of filters is important. Typically, this is characterised by looking at the response to a step change in the input voltage. Again, this depends on the order and response type and there are trade-offs in desirable properties. Filter circuit design There are many different circuits which can be configured to implement a desired filter response (for example Sallen-Key, multiple feedback and state variable). These have different non-ideal characteristics which might need to be taken into consideration and balanced against factors such as cost and complexity. When designing a filter, the bandform and cut off frequency are usually straightforward to determine from the application. The order, response type (Butterworth, Chebyshev) and circuit implementation choices will be based on the performance requirements – for example, how close are unwanted signals 47 Fig.4. (left) Sallen-Key second-order low-pass filter. C2 Vin R1 R2 – C2 R4 Vout Digipot Digipot W W Electronically Controlled – Part 8 8 Vin Resistance Electronically Controlled Resistance – Part Fig.5. (right) B B Electronically Controlled ResistanceUnity-gain – Part 8 𝑓𝑓! =𝑓𝑓!𝐹𝐹"=𝑓𝑓# 𝐹𝐹R" 𝑓𝑓# C1 R3 R1 2 C1 Sallen-Key low𝑓𝑓! = 𝐹𝐹" 𝑓𝑓with # pass filter Electronically Controlled Resistance – Part 8 digipot cut𝑅𝑅$ 𝐴𝐴 =𝐴𝐴1= + 1 + 𝑅𝑅$ 𝑓𝑓! =off𝐹𝐹"frequency 𝑓𝑓# 𝑅𝑅% 𝑅𝑅 𝑅𝑅$ % control. 𝐴𝐴 = 1 + 𝑅𝑅% + – Vout + 𝑅𝑅$ be obtained with the RC to wanted ones and how much do they values than can should dominate the digipot parasitics, = 1 + has a maximum Q of 0.5, need to be attenuated. filter,𝐴𝐴which so something 1 1 around 10nF may be the 𝑅𝑅% 𝑓𝑓! =smallest For the various circuit implementations and is often lower. capacitor value that should be 𝑓𝑓! = 2𝜋𝜋*𝑅𝑅& 𝑅𝑅' 𝐶𝐶 & 𝐶𝐶 1 & 𝑅𝑅 'a&𝐶𝐶real & 𝐶𝐶& design the details of there are equations relating the component The other used,2𝜋𝜋*𝑅𝑅 but for 𝑓𝑓! = design equations for this values to the resonant frequency and Q. circuit are: 2𝜋𝜋*𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& individual digipot devices can be checked The required response type determines the on datasheets. 1 𝑓𝑓! = Q and frequency-scaling factor. These can 2𝜋𝜋*𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 𝑅𝑅' 𝐶𝐶 *𝑅𝑅&*𝑅𝑅 & 𝐶𝐶 be found in filter design tables published & 𝑅𝑅 '&𝐶𝐶simplifications & 𝐶𝐶& 𝑄𝑄 =𝑄𝑄 = Sallen-Key 𝑅𝑅 𝐶𝐶 + 𝑅𝑅 𝐶𝐶 + 𝑅𝑅 𝐴𝐴) in various places. A well-known example One approach to− simplifying the Sallen& 𝑅𝑅 & & 𝐶𝐶& + ' 𝑅𝑅 & ' 𝐶𝐶& + & 𝐶𝐶𝑅𝑅 ' (1 *𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& & 𝐶𝐶' (1 − 𝐴𝐴) 𝑄𝑄 = of this is the Active Filter Cookbook by Key equations is to use equal component 𝑅𝑅& 𝐶𝐶& + 𝑅𝑅' 𝐶𝐶& + 𝑅𝑅& 𝐶𝐶' (1 − 𝐴𝐴) Don Lancaster, which was first published values R = R1 = R2, and C = C1 = C2, 𝑅𝑅' 𝐶𝐶 *𝑅𝑅 &is & 𝐶𝐶& resonant frequency. in 1975 and is described as the best-selling Where f which gives: the 0 𝑄𝑄 = (1 1 𝐶𝐶 + 𝑅𝑅 𝐶𝐶 + 𝑅𝑅 𝐶𝐶 − 𝐴𝐴) book on active filter design. Another 𝑅𝑅These equations are quite cumbersome, & & ' & & ' 𝐹𝐹 𝑓𝑓 = 𝑓𝑓 = = 1 source is Active Low-Pass Filter Design, an so simplifications are often made, which " # 𝐹𝐹" 𝑓𝑓# != 𝑓𝑓!2𝜋𝜋𝜋𝜋𝜋𝜋 2𝜋𝜋𝜋𝜋𝜋𝜋 1 application note by Jim Karki from Texas we will 𝐹𝐹discuss = " 𝑓𝑓# = 𝑓𝑓! below. 2𝜋𝜋𝜋𝜋𝜋𝜋 1 Instruments (SLOA049 – see: https://bit. 𝑄𝑄 =𝑄𝑄 = 1 ly/pe-apr23-ti). An alternative to tableDigipots with1 Sallen-Key filters 3 − 3𝐴𝐴− 𝐴𝐴 1 𝐹𝐹 𝑓𝑓# = 𝑓𝑓! = assisted manual calculations is to use a 𝑄𝑄 2𝜋𝜋𝜋𝜋𝜋𝜋 = To "use the Sallen-Key with digipot control 3 − 𝐴𝐴 filter design app or online tool. These make we need to be able to control the cut-off This provides very simple design Electronically Controlled Resistance –equations Part 8 but does not allow the overall 1 by varying things easy but may restrict the options frequency just the resistors. 𝑄𝑄 = Electronically Controlled Resistance – Part1 8 for exactly how the filter is implemented. The capacitors gain of the filter1to be set independently of 3 − 𝐴𝐴 should be chosen based 𝐹𝐹 𝑓𝑓 = = 𝑓𝑓#𝑓𝑓 ==𝑓𝑓 𝐹𝐹!2𝜋𝜋𝜋𝜋𝐶𝐶 ( 𝑓𝑓 !!= " 𝑓𝑓 # Filters represent a huge ‘design space’ on the midpoint of the1required frequency ( #𝐹𝐹the Q value. 𝑛𝑛 circuit can be designed &The 2𝜋𝜋𝜋𝜋𝐶𝐶 𝑓𝑓! = 𝐹𝐹√𝑓𝑓#& √𝑛𝑛 𝑓𝑓# = 𝑓𝑓The of possibilities – bandform, response control𝐹𝐹(range. by choosing a"required response, which ! = resonant and hence cut2𝜋𝜋𝜋𝜋𝐶𝐶 type, order, circuit implementation and off frequency is set by &R√1𝑛𝑛and R2, which sets the Q, and choosing R3 and R4 to √𝑛𝑛𝑅𝑅 𝑛𝑛 1 𝑄𝑄 = = $√gain so on. To keep things manageable for need to be independently controlled, obtain (A) for that Q. 𝐴𝐴 = 1𝑄𝑄+the 2 2 𝑅𝑅required 𝐹𝐹( 𝑓𝑓# = 𝑓𝑓! = $ 𝑛𝑛 𝑅𝑅 √ %1 + the remainder of this article on using which implies use of two digipots in The Q could be set independently of the 2𝜋𝜋𝜋𝜋𝐶𝐶 𝑛𝑛 𝐴𝐴 = √ 𝑄𝑄 = & 2 we have discussed digipots with filters we will just look at rheostat mode. As frequency with𝑅𝑅a% digipot, as mentioned second-order low-pass Sallen-Key Filters. previously,√digipot resistance values are above, but the gain variation may need to 𝑛𝑛 𝑄𝑄 =particularly accurate,1which Sallen-Key filters are widely used, and often not be compensated 1 1 for by another variable 2 1 = 1 =𝑅𝑅 = = 5181 tools are available to help design them will affect the accuracy 𝑅𝑅with which the gain stage. The frequency is set by = = 5181 2𝜋𝜋𝑓𝑓2𝜋𝜋𝑓𝑓 𝑛𝑛 √𝑛𝑛𝑓𝑓2𝜋𝜋 852 × 15𝑛𝑛𝑛𝑛 × √5.099 ! =× ! 𝐶𝐶& √ 1 𝐶𝐶 1 1 2𝜋𝜋 × 852 × 15𝑛𝑛𝑛𝑛 × √5.099 ! & (select the required component values). cut-off frequency can be controlled. Use choosing C and controlling R with two 2𝜋𝜋*𝑅𝑅 𝑅𝑅 𝐶𝐶 𝐶𝐶 𝑓𝑓 = & ' & & 𝑅𝑅 = = = 5181 ! 2𝜋𝜋𝑓𝑓! 𝐶𝐶of Low-pass filters are commonly required in would usually digipots2𝜋𝜋*𝑅𝑅 in rheostat set to the same 2𝜋𝜋digipot × 852 ×device 15𝑛𝑛𝑛𝑛 × √5.099 & 𝑅𝑅' 𝐶𝐶& 𝐶𝐶mode & & √a𝑛𝑛 dual microcontroller circuits for anti-aliasing be a good option. resistance to set the resonant frequency. 1 1 𝑅𝑅 = = We are probably less likely=to5181 and reconstruction filters before/after want to The resonant 𝑅𝑅 𝑅𝑅 frequency is calculated 2𝜋𝜋𝑓𝑓! 𝐶𝐶& √𝑛𝑛 2𝜋𝜋 × 852 × 15𝑛𝑛𝑛𝑛 × √5.099 ADCs and DACs, where cut-off frequency control the Q with a digipot – in most from required cut-off frequency using 𝐷𝐷 =𝐷𝐷the 𝑆𝑆𝑅𝑅 = 𝑆𝑆& 𝐶𝐶& 𝐶𝐶 *𝑅𝑅& 𝑅𝑅')* 𝑅𝑅)* 𝑅𝑅 programmability may be desirable. cases the requirement would be𝑄𝑄for the frequency-scaling factor. = a 𝑅𝑅 𝐶𝐶 *𝑅𝑅 ' − & 𝐶𝐶𝐴𝐴) & 𝐷𝐷 = 𝑆𝑆 𝑅𝑅 𝐶𝐶 + 𝑅𝑅' 𝐶𝐶& + 𝑅𝑅& 𝐶𝐶&' (1 fixed response shape gain variations discussed above 𝑅𝑅)* with a variable&𝑄𝑄&= 𝑅𝑅The & 𝐶𝐶& + 𝑅𝑅' 𝐶𝐶& + 𝑅𝑅& 𝐶𝐶' (1 − 𝐴𝐴) cut-off frequency. However, it would can be avoided by using a fixed gain. Sallen-Key low-pass filter 𝑅𝑅 be possible This requires at least the two resistors Fig.4 shows a Sallen-Key low-pass filter. 𝐷𝐷 = 𝑆𝑆 to use a digipot to set the 𝑅𝑅)* amplifier gain (via R3 and R4) and hence or the two capacitors to have different It comprises a frequency-dependent 1 Resistance circuit – Part 8formed by R , R , C and C , and used variant of the make Q programmable. We discussed use 𝐹𝐹" 𝑓𝑓#values. = 𝑓𝑓! =A commonly 1 2 1 2 1 2𝜋𝜋𝜋𝜋𝜋𝜋 Sallen-Key of digipots to control op amp amplifier a non-inverting op amp amplifier. The 𝐹𝐹" 𝑓𝑓# = 𝑓𝑓!filter = is the unity-gain version 2𝜋𝜋𝜋𝜋𝜋𝜋 𝑓𝑓! = 𝐹𝐹" 𝑓𝑓#gain (A) is set by R and R , shown in Fig.5, which also shows how gain in Part 5. amplifier 3 4 1 the digipots are Use of digipots may introduce and is given by: 𝑄𝑄 = 1 used. 3− 𝑄𝑄 𝐴𝐴 =design simplification approach Another limitations on the filter design. For 3 − 𝐴𝐴 𝑅𝑅$ is to set equal resistors and capacitors example, their parasitic capacitance is 𝐴𝐴 = 1 + 𝑅𝑅% with ratio n, that is R = R1 = R2, and C2 = likely to be higher than the same filter using fixed resistors. Parasitic capacitance nC1 which gives: 1 is the unwanted capacitance inherent in𝐹𝐹( 𝑓𝑓# = 𝑓𝑓! = The frequency-dependent circuit is 1 2𝜋𝜋𝜋𝜋𝐶𝐶 𝐹𝐹( 𝑓𝑓# = 𝑓𝑓! =& √𝑛𝑛 structure of the pins and circuitry of the similar to a two-stage RC filter, but with 2𝜋𝜋𝜋𝜋𝐶𝐶& √𝑛𝑛 1 digipot device. This will limit the upper C connected to positive feedback from 𝑓𝑓! =2 𝑛𝑛 √ frequencies than can be used or accurately the2𝜋𝜋*𝑅𝑅 amplifier, rather than to ground. This & 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 𝑄𝑄 = controlled. Frequency-setting capacitors allows the circuit to have much higher Q 2𝑄𝑄 = √𝑛𝑛 2 48 Practical Electronics | April | 2023 𝑄𝑄 = *𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 1 1 ronically Controlled Resistance – Part 8 𝑓𝑓! = 𝐹𝐹" 𝑓𝑓# trolled Resistance – Part 8 𝑓𝑓! = 𝐹𝐹" 𝑓𝑓# 𝐴𝐴 = 1 + 𝑓𝑓! = 𝑅𝑅$ 𝑅𝑅% 1 𝑅𝑅$ 𝐴𝐴 = 1 + 𝑅𝑅% 𝑓𝑓! = 1 2𝜋𝜋*𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 2𝜋𝜋*𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 𝑄𝑄 = 𝐴𝐴 = 1 + *𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 𝑅𝑅& 𝐶𝐶& + 𝑅𝑅' 𝐶𝐶& + 𝑅𝑅& 𝐶𝐶' (1 − 𝐴𝐴) 𝑓𝑓! = 𝑄𝑄 = 𝑅𝑅$ 𝑅𝑅% 1 2𝜋𝜋*𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& Fig.6. LTspice schematic for 1kHz unity-gain Sallen-Key low-pass filter. *𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 𝑅𝑅& 𝐶𝐶& + 𝑅𝑅' 𝐶𝐶& + 𝑅𝑅& 𝐶𝐶' (1 − 𝐴𝐴) 𝐹𝐹" 𝑓𝑓# = 𝑓𝑓! = 1 2𝜋𝜋𝜋𝜋𝜋𝜋 1 3 − 𝐴𝐴 ripple size below the peak gain, which next represents a larger frequency change. in this case is the point where it crosses This in turn means that it is less likely 0dB as it transitions into the stopband. that exactly the right resistance value will 1 at the higher frequency end This occurs at 1kHz, as designed. 𝐹𝐹( 𝑓𝑓# be = 𝑓𝑓available ! = 2𝜋𝜋𝜋𝜋𝐶𝐶& √𝑛𝑛 of the programmable range. As discussed previously (see Part 5 in Setting the digipot code PE, January Example design In a typical programmable filter application, 1 √𝑛𝑛 2023) digipots can be modelled 𝑄𝑄two = resistors R and R such that the as there are likely to be a set of required cut-of Consider𝑄𝑄a = filter of Chebyshev type with A B 3 − 𝐴𝐴 2 frequencies. For these cut-off frequencies 2dB passband ripple and 1kHz cut-off. If total resistance RA + RB = RAB where RAB 1 = 𝑓𝑓! = to be implemented in a circuit like that we look it up, Q𝐹𝐹(=𝑓𝑓#1.129 and Fs =√0.907 is the resistance between the terminals A 2𝜋𝜋𝜋𝜋𝐶𝐶 & 𝑛𝑛 in Fig.5 the required resistor values must and B and the specified resistance of the and using the equal-resistor unity-gain fall within the range of resistance1values digipot. In1rheostat mode we use just one Sallen-Key circuit1we need n = 4Q2 = √𝑛𝑛 𝑅𝑅 = combined = = 5181 𝐹𝐹( 𝑓𝑓# Choosing = 𝑓𝑓! = available from the digipot, these say from terminal B 5.099. C = 15nF gives C = 𝑄𝑄 = 1 2 2𝜋𝜋𝑓𝑓! 𝐶𝐶& √𝑛𝑛 2𝜋𝜋 of 2𝜋𝜋𝜋𝜋𝐶𝐶& √𝑛𝑛 × 852 × resistances, 15𝑛𝑛𝑛𝑛 × √5.099 2 need f = with fixed capacitor values. This means to the wiper (as drawn in Fig.5). For a 76.48nF. For 1kHz cut-off we 0 that very wide frequency ranges will not digipot with S steps we need a digital code Fsfc = 0.852 × 1000 = 852. We can then √𝑛𝑛 be possible, but something from 10:1 to D to set a resistance value R as follows: calculate R𝑄𝑄 as: = 2 100:1 should be possible. 𝑅𝑅 1 1 𝐷𝐷 = 𝑆𝑆 basic filter calculations discussed 𝑅𝑅 = = =The 5181 𝑅𝑅)* 2𝜋𝜋𝑓𝑓! 𝐶𝐶& √𝑛𝑛 2𝜋𝜋 × 852 × 15𝑛𝑛𝑛𝑛 × √5.099above determine the required resistance values, but these need to be mapped to the The actual resistance obtained is: 1 1 digipot codes giving the nearest resistance = = = 5181 𝐷𝐷 2𝜋𝜋𝑓𝑓! 𝐶𝐶& √𝑛𝑛 2𝜋𝜋 × 852 × 15𝑛𝑛𝑛𝑛 × √5.099 values. The exact resistance required may 𝑅𝑅 = 𝑅𝑅)* 𝑆𝑆 𝑅𝑅 not be available from the digipot, leading 𝐷𝐷 = 𝑆𝑆 𝑅𝑅 )* to errors in the frequency setting. The In some cases, there may be a significant Fig.6 shows an LTspice schematic of the more positions the digipot has the more difference between the required and filter implementation. The simulation 𝑅𝑅 likely the frequency can be set close to obtained resistance, in other cases they results (AC to plot frequency 𝐷𝐷 =analysis 𝑆𝑆 𝑅𝑅)* the desired value. will be close. For example, to set a 10kΩ, response) for this circuit in Fig.7 show the The reciprocal nature of the frequency 256-step digipot to 5181Ω (from the above gain is 0dB at low frequencies (unity gain). to resistance relationship means that at example) requires a digital code of 256 × The gain peaks at +2dB (this is the 2dB higher frequencies (lower resistance) each (10000 / 5181) = 133. The actual resistance passband ripple). The cut-off frequency step in resistance from one code to the is 5195Ω , an error of just 0.3%. For a for this type of filter is defined as the 100kΩ, 256-step digipot the code required is 13 and the resistance is 5078Ω, a 2% error. Smaller resistances may produce larger errors with a given digipot. For example, 518.1Ω for a 10kHz cut-off with the above circuit requires codes 13 and 1 with resistance errors of 2% and 25% respectively for the 10kΩ and 100kΩ digipots. This assumes a perfectly accurate digipot, but the RAB value itself may be subject to quite a large tolerance, for example 20% in some cases. *𝑅𝑅& 𝑅𝑅' 𝐶𝐶& 𝐶𝐶& 𝑅𝑅& 𝐶𝐶& + 𝑅𝑅' 𝐶𝐶& + 𝑅𝑅& 𝐶𝐶' (1 − 𝐴𝐴) To design with this approach the1required 𝐹𝐹" 𝑓𝑓#Q,=which 𝑓𝑓! = in turn sets response type sets the 2𝜋𝜋𝜋𝜋𝜋𝜋 the capacitor ratio (n). The base capacitance value, n and the 1calculated 1 resonant 𝑄𝑄 the = resistor value. 𝐹𝐹" 𝑓𝑓# = 𝑓𝑓!used = to set frequency are 3 − 𝐴𝐴 2𝜋𝜋𝜋𝜋𝜋𝜋 𝑄𝑄 = 𝑄𝑄 = Design tools Fig.7. Simulation results for the circuit in Fig.6. Practical Electronics | April | 2023 The filter design calculations above, and the associated need to obtain the correct Q and frequency-scaling factor can be avoided by using a filter design app or online utility. These tools may reduce the options for component selection compared with manual 49 Fig.8. (left) FilterLab bandform and response type setting. Fig.9. (right) FilterLab filter parameter settings. Fig.10. (above) FilterLab circuit settings. Fig.11. (right) Example FilterLab result. design, which could be a problem in the context of digipot-controlled circuits. We need to be able to find a set of resistor values to set different cut-off frequencies using a circuit with the fixed capacitor values and op amp circuit gain. This means we have to be able to set the capacitor values and let the tool calculate the resistor values for a fixed-gain circuit such as the unity-gain Sallen-Key discussed above. Unlike the simplified approach above, it is not necessary to have equal resistors. In fact, by using different resistor values (as calculated by the tool) the response shape can be changed as well as the cutoff frequency, allowing the shape as well as cut-off to be programmed. The way the numbers work means that if a range of response types is required the range of cut-off frequencies possible with a given digipot will be smaller than with a fixed response type. As was seen in the equal-resistor example design above, the capacitor ratio can influence the Q. The resistors do not have to be equal but similar values will make it easier to make use of a dual digipot. In general, the feedback capacitor (C2 in Fig.5) will be larger than the capacitor at the op amp input (C1). Unlike the above example, standard capacitor values should be used for a real design. FilterLab One filter design tool that allows you to set capacitor values is FilterLab from Microchip – see: https://bit.ly/pe-apr23-mc To design a filter using this app, select Filter > Design from the menu and step through the three tabs in the dialog (see Fig.8 to Fig.10). The first tab is used to select the bandform and response type. Simulation files Fig.12. LTspice schematic for Sallen-Key filter with digipot control. 50 Most, but not every month, LTSpice is used to support descriptions and analysis in Circuit Surgery. The examples and files are available for download from the PE website. Practical Electronics | April | 2023 Here we have selected Chebyshev lowpass as in the example above. The second tab sets the filter parameters, here we selected ‘Force filter order’ – this is to help make sure the tool uses the required circuit to implement the design. We select 1000Hz cut-off and –2dB for the passband to match the 2dB ripple Chebyshev design discussed above. The third tab allows the circuit type to be selected (Sallen-Key in this case) and the capacitor values to be set, so they are fixed in the circuit implementation. To do this, click on both capacitors and select the value from the dropdown list. The result is shown in Fig.12 – the schematic of the filter created by the app. For full details of using FilterLab consult the manual on the download page. Example design Fig.13. Simulation results from the circuit in Fig.12. FilterLab was used to create three more circuits with different cut-offs. These can be simulated using all the code combinations in one sweep simulation we can use the circuit in Fig.12. Using the procedure described above, the LTspice table function which uses an index to look up the digipot codes were calculated for a 256-step 10kΩ digipot for corresponding value. For four configurations we need index the following frequencies: values 1 to 4 which can be achieved by defining a parameter R1 codes: 140 called FSET (frequency set), sweeping it in steps of 1 from 1 to 98 49 33 4 and using this in the look up. For example, for R1: R2 codes: 239 167 84 56 700Hz 1kHz 2kHz 3kHz .param Fset=1 RAB=100k N=256 In LTspice we can use a behavioural resistance (as used in R = table({Fset},1,140,2,98,3,49,4,33)*{RAB}/{S} previous parts) to calculate the actual digipot resistance using the formula above with the RAB resistance and number of digipot The results of the simulation are shown in Fig.13 and confirm that the filter responses are as designed. steps as parameters (RAB and S respectively). To run through GET T LATES HE T CO OF OU PY R TEACH -IN SE RIES AVAILA BL NOW! E Order direct from Electron Publishing PRICE £8.99 (includes P&P to UK if ordered direct from us) EE FR -ROM CD ELECTRONICS TEACH-IN 9 £8.99 FROM THE PUBLISHERS OF GET TESTING! Electronic test equipment and measuring techniques, plus eight projects to build FREE CD-ROM TWO TEACH -INs FOR THE PRICE OF ONE • Multimeters and a multimeter checker • Oscilloscopes plus a scope calibrator • AC Millivoltmeters with a range extender • Digital measurements plus a logic probe • Frequency measurements and a signal generator • Component measurements plus a semiconductor junction tester PIC n’ Mix Including Practical Digital Signal Processing PLUS... YOUR GUIDE TO THE BBC MICROBIT Teach-In 9 – Get Testing! Teach-In 9 A LOW-COST ARM-BASED SINGLE-BOARD COMPUTER Get Testing Three Microchip PICkit 4 Debugger Guides Files for: PIC n’ Mix PLUS Teach-In 2 -Using PIC Microcontrollers. In PDF format This series of articles provides a broad-based introduction to choosing and using a wide range of test gear, how to get the best out of each item and the pitfalls to avoid. It provides hints and tips on using, and – just as importantly – interpreting the results that you get. The series deals with familiar test gear as well as equipment designed for more specialised applications. The articles have been designed to have the broadest possible appeal and are applicable to all branches of electronics. The series crosses the boundaries of analogue and digital electronics with applications that span the full range of electronics – from a single-stage transistor amplifier to the most sophisticated microcontroller system. There really is something for everyone! Each part includes a simple but useful practical test gear project that will build into a handy gadget that will either extend the features, ranges and usability of an existing item of test equipment or that will serve as a stand-alone instrument. We’ve kept the cost of these projects as low as possible, and most of them can be built for less than £10 (including components, enclosure and circuit board). © 2018 Wimborne Publishing Ltd. www.epemag.com Teach In 9 Cover.indd 1 01/08/2018 19:56 PLUS! You will receive the software for the PIC n’ Mix series of articles and the full Teach-In 2 book – Using PIC Microcontrollers – A practical introduction – in PDF format. Also included are Microchip’s MPLAB ICD 4 In-Circuit Debugger User’s Guide; MPLAB PICkit 4 In-Circuit Debugger Quick Start Guide; and MPLAB PICkit4 Debugger User’s Guide. ORDER YOUR COPY TODAY: www.electronpublishing.com Practical Electronics | April | 2023 51