Resistors aren’t resistors
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 another time. 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 6-mm leads) might be 14 nH of series inductance and 1-2 pF parallel capacitance.
Now, if you plot this simplified model versus frequency, you should see the following idealised impedance plot.
Figure 3: An idealised impedance plot of a real resistor shows the different points where resistance dominates, capacitance reduces impedance, and inductance increases impedance.
At lower frequencies… (continues)
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 20 dB/decade. The resistor now becomes a capacitor. The breakpoint occurs here.
There will be a point where the capacitive reactance equals the inductive reactance. For a brief moment, the impedance will become purely resistive once again (though at a much lower resistance value). This series resonance occurs at this breakpoint.
After this point, the series lead inductance becomes dominant, and the poor resistor becomes an inductor. Its impedance plot rises at 20 dB/decade.
To help illustrate this, I measured a carbon-composition resistor with 1/4-inch leads and plotted the following.
Figure 4: The measured impedance plot of a 1kΩ carbon-composition resistor with short leads.
The frequency varied from 1 MHz to 450 MHz, so you can’t see the impedance increasing because of series inductance. At 100 MHz, however, you can see the impedance of the 1 kΩ resistor has dropped to about 730 Ω. At 300 MHz, it’s just 330 Ω.
Even when using surface-mount components, where the series inductance is typically 1-2 nH and the parallel capacitance is 0.2-0.4 pF, this can still affect the measured value of impedance at high frequencies into the hundreds of megahertz.
By understanding that parasitic elements of real components can affect the impedance, you can see why keeping lead lengths and circuit traces short and why surface-mount components are superior for high-frequency designs.
Kenneth Wyatt is an independent consultant and specialist in electromagnetic compatibility (EMC) design, test and troubleshooting.
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