Path: EDN Asia >> Design Ideas >> IC/Board/Systems Design >> How to synthesise variable resistors with hyperbolic taper
IC/Board/Systems Design Share print

How to synthesise variable resistors with hyperbolic taper

01 Feb 2016  | T Flaig

Share this page with your friends

In adjustable, frequency-selective RC networks, the corner frequencies of the network is determined by the reciprocal of an RC product, ωC=1/RC. If the adjustable elements are potentiometers with a linear-control characteristic—that is, taper—R(α)=αRP, where α is the normalized wiper position, 0&α&1, and RP is the potentiometer's end-to-end resistance, then the corner frequencies are reciprocal functions of the potentiometer's wiper position, and the frequency scale compresses at the high end of the adjustment range. This situation is usually undesirable because it complicates adjustment of the network at the high end. To make the frequency scale linear requires a control element with a hyperbolic taper—that is, something in the form R(α)=RP/(A+αB). Such variable resistances are not generally available from manufacturers, but you can synthesise them using a linear taper potentiometer and a few other components.

Figure 1: This simple circuit synthesises a grounded variable resistance with a hyperbolic-control characteristic.

Figure 1 shows a simple circuit for producing a ground-referenced variable resistance having the desired hyperbolic-control characteristic. Analysis of this circuit yields the following relationship between the control setting and the resistance from Node 1 to ground: R1-0(α)=R1R2RP/(R1R2+R1RP+αR2RP)0&α&1. If you use this resistance in series or in parallel with a capacitor, the resulting corner frequency will be a linear function of α: ωC=(R1R2+R1RP+αR2RP)/R1R2RPC. The minimum and maximum values for R1-0 are R1-0MIN=R1R2RP/(R1R2+R1RP+R2RP) and R1-0MAX=R2RP/(R2+RP).

To design this circuit for specific values of R1-0MIN and R1-0MAX, choose RP>R1-0MAX and then compute R1=R1-0MAX R1-0MIN/(R1-0MAX–R1-0MIN) and R2=RPR1-0MAX/(RP–R1-0MAX).

Figure 2: You can realise a floating variable resistance, with hyperbolic taper, with this circuit. Note that fixed resistors with the same number are matched pairs.

1 • 2 Next Page Last Page

Want to more of this to be delivered to you for FREE?

Subscribe to EDN Asia alerts and receive the latest design ideas and product news in your inbox.

Got to make sure you're not a robot. Please enter the code displayed on the right.

Time to activate your subscription - it's easy!

We have sent an activate request to your registerd e-email. Simply click on the link to activate your subscription.

We're doing this to protect your privacy and ensure you successfully receive your e-mail alerts.

Add New Comment
Visitor (To avoid code verification, simply login or register with us. It is fast and free!)
*Verify code:
Tech Impact

Regional Roundup
Control this smart glass with the blink of an eye
K-Glass 2 detects users' eye movements to point the cursor to recognise computer icons or objects in the Internet, and uses winks for commands. The researchers call this interface the "i-Mouse."

GlobalFoundries extends grants to Singapore students
ARM, Tencent Games team up to improve mobile gaming

News | Products | Design Features | Regional Roundup | Tech Impact