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Signals10 min read
Bode Plots
Read gain and phase across frequency without treating the graph as a mysterious set of slopes.
Mental model
A Bode plot is a map of what a circuit does to slow, medium and fast changes. It shows which frequencies pass and which are weakened.
A first-order low-pass stays near 0 dB at low frequency, reaches about −3 dB and −45° at fc, then approaches a −20 dB/decade slope and −90° phase.UNDERSTAND THE BEHAVIOR
01
A Bode magnitude plot compresses a huge range of frequencies and gains into a readable form. The horizontal axis is logarithmic, so equal distances represent equal multiplication factors such as ×10.
02
Decibels turn multiplication into addition. Cascading a −20 dB stage with a +6 dB stage gives −14 dB overall. For voltage ratios, use 20 log10; for power ratios, use 10 log10.
03
Poles bend the response downward and zeros bend it upward. Real transitions are smooth, but straight-line approximations make first analysis fast.
Why it matters
Bode plots let you predict bandwidth, noise rejection and feedback stability before looking at a time-domain waveform.
Core ideas
Magnitude is usually shown in decibels on a logarithmic frequency axis.
A first-order pole adds a −20 dB/decade slope.
At a first-order cutoff frequency, gain is −3 dB.
Key equationsGain(dB) = 20 log₁₀|Vout/Vin|Voltage ratio = 10^(dB/20)
EXAMPLE
Worked example — interpreting −20 dB
1At 10 kHz, a circuit has −20 dB gain.
2Voltage ratio = 10^(−20/20) = 0.1.
3For a 2 V input, output is 0.2 V.
4The voltage amplitude is reduced by a factor of ten.
Common mistake
−3 dB is not half the voltage. It is about 0.707 times the voltage and half the power.
RememberMagnitude is usually shown in decibels on a logarithmic frequency axis.
Practice and check your understanding
Try each question before opening the worked answer.
1. An amplifier changes 0.1 V into 1 V. Find the voltage gain in dB.
Show answer and reasoning
The voltage ratio is 1/0.1 = 10. Gain = 20 log10(10) = 20 dB. Use the same amplitude convention for both voltages, such as RMS for both.
2. Far above cutoff, what additional attenuation does a first-order low-pass add from 10 kHz to 100 kHz?
Show answer and reasoning
That is one decade. The asymptotic slope is −20 dB per decade, so the output-to-input amplitude ratio falls by approximately a factor of ten.