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How to synthesise variable resistors with hyperbolic taper

01 Feb 2016  | T Flaig

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You can extend the basic circuit of figure 1 to produce a floating variable resistance with hyperbolic taper (figure 2). The value of the floating resistance between nodes 1 and 2 is R1-2(α)=2R1R2RP/(2R1R2+R1RP+2αR2RP)0&α&1, and the minimum and maximum values for R1-2 are R1-2MIN=2R1R2RP/(2R1R2+R1RP+2R2RP) and R1-2MAX=2R2RP/(2R2+RP). To design the circuit of figure 2 for specific values of R1-2MIN and R1-2MAX, choose RP>R1-2MAX and then compute R1=R1-2MAXR1-2MIN/(R1-2MAX–R1-2MIN) and R2=½RPR1-2MAX/(RP–R1-2MAX). Note that the value of the R3 resistors does not directly affect the value of R1-2(α). You should choose resistors that are large enough to not excessively load the op-amp outputs.

Figure 3: The basic circuits of figures 1 and 2 have been used in the design of a bridged-T notch filter with a variable notch centre frequency and a linear frequency scale.

Figure 3 illustrates the application of the circuits in figure 1 and figure 2 to the design of an adjustable bridged-T notch filter with a linear frequency scale. The filter has a notch centre frequency that is adjustable from 50 to 1000Hz and a notch depth of –20 dB. These requirements and the choice of 0.1-µF capacitors for C1 and C2 dictate that R1-0 varies from 375 to 7503Ω and that R1-2 varies from 6752 to 135,047Ω. (A side benefit of using this technique is that it frees the designer from the restrictions of the limited number of standard end-to-end resistance values that potentiometer manufacturers offer.)

Figure 4: The Spice-simulated notch centre frequency for the circuit of Figure 3 versus the normalized wiper position shows that the notch centre frequency is a linear function of the control position.

Figure 4 plots the Spice-simulated notch centre frequency for the circuit of figure 3 against the normalized wiper position. The notch centre frequency is a linear function of the control position.

About the author
T Flaig contributed this article.

This article is a Design Idea selected for re-publication by the editors. It was first published on January 8, 2009 in

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