Learning Library · Frequency domain · 1

Bode plots: how a circuit responds to frequency

Filters, amplifiers, and power-supply control loops all treat different frequencies differently. A Bode plot puts that behaviour on one chart: how much signal gets through, and how much it is delayed, at every frequency.

Reading the two plots

Both plots share a logarithmic frequency axis, so each grid step is ten times the last: 10 Hz, 100 Hz, 1 kHz, and so on. A log axis keeps a span of five decades readable on one chart.

Magnitude (top) is the output amplitude divided by the input amplitude, expressed in decibels. Phase (bottom) is how far the output wave is shifted in time relative to the input, in degrees of one cycle.

Decibels in one table

Gain	Voltage ratio	Power ratio
0 dB	1	1
−3 dB	0.707	0.5
−6 dB	0.5	0.25
−20 dB	0.1	0.01
−40 dB	0.01	0.0001

What the RC filter is doing

A capacitor's opposition to current falls as frequency rises. In the low-pass filter the capacitor sits across the output, so at high frequencies it shunts the signal away. In the high-pass version the capacitor sits in the signal path, so it blocks low frequencies and DC.

The cutoff frequency f_c is where the output is down 3 dB, to 70.7 % of the input voltage and half the power. At f_c the phase shift is exactly 45°. Beyond it, a single RC stage rolls off at 20 dB per decade: every tenfold step in frequency cuts the output to a tenth.

Try this

• Put the probe on the cutoff. The gain reads −3.01 dB and the phase reads −45° for the low-pass.
• Move the probe to ten times f_c. The gain is close to −20 dB, and the output wave is about a tenth the size of the input.
• Double the capacitance. The whole curve slides left by a factor of two, because f_c halves.
• Switch to high-pass. The plot mirrors: low frequencies are blocked, and the output now leads the input instead of lagging it.

Measuring a Bode plot

The classic method is a frequency sweep. A function generator drives the circuit with a sine wave, a two-channel oscilloscope measures input and output, and at each frequency you record the amplitude ratio and phase difference. Many current oscilloscopes automate this with a frequency-response analysis function that sweeps a built-in or connected generator and draws the plot directly.

Beyond filters, Bode plots are the standard tool for checking the stability of feedback loops, such as the control loop in a switching power supply. There, the gain and phase margins read off the plot show how close the loop is to oscillating.

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