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Resistors are not resistors at high frequencies

08 Nov 2013  | Kenneth Wyatt

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At high frequencies, resistors are not resistors.

Many designers don't realise that parasitic elements in real components affect their values. When frequencies reach hundreds of megahertz, basic components such as resistors, inductors, and capacitors take on non-ideal characteristics. Such changes can become critical when you design filters or attempt to optimise power delivery networks, bypass networks, or bias circuits.

We will discuss capacitors and inductors in later posts. For now, let's talk about the lowly resistor. Here's the plot of an ideal impedance of a resistor, which, as you might expect, is a straight line.

Figure 1: The impedance plot of an ideal resistor versus frequency shows the same value at all frequencies.

Now let's consider a carbon-composition resistor with short leads. If you add the parasitic inductance of the leads and parallel capacitance between the end caps, you should get this simplified model at high frequencies.

Figure 2: A simplified model of a typical resistor at high frequencies shows parallel capacitance and series inductance.

Typical values for the carbon-composition resistor (with 1/4-inch (convert to mm except for displays) leads) might be 14nH of series inductance and 1-2pF parallel capacitance.

Now, if you plot this simplified model versus frequency, you should see the following idealized impedance plot.

Figure 3: An idealized impedance plot of a real resistor shows the different points where resistance dominates, capacitance reduces impedance, and inductance increases impedance.

At lower frequencies, the plot would be purely resistive (horizontal line). But as frequency increases, the parallel capacitance dominates, and the impedance starts to drop at 20dB/decade. The resistor now becomes a capacitor. The breakpoint occurs here.

After this point, the series lead inductance becomes dominant, and the poor resistor becomes an inductor. Its impedance plot rises at 20dB/decade.

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