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Electronics

How to read a Bode plot

A Bode plot shows how a circuit's gain changes with frequency: gain in decibels up the side, frequency along the bottom on a logarithmic scale. On it, a simple RC filter becomes two straight lines meeting at a corner: flat in the pass band, then falling 20 dB per decade past the corner frequency, where the real curve sits at −3 dB.

Why decibels and a log axis

Filters shrink signals by huge ratios: a half, a tenth, a thousandth. Decibels turn those ratios into equal steps, and the logarithmic frequency axis gives every decade (10 Hz to 100 Hz, 100 Hz to 1 kHz) the same width. Together they straighten curves into lines you can draw with a ruler.

Voltage ratioDecibels
0.01−40 dB
0.1−20 dB
0.5−6 dB
0.707−3 dB
10 dB
10+20 dB

Each ×10 is +20 dB, and multiplying ratios means adding decibels: ×20 is 20 + 6 = 26 dB.

Live experiment

Draw a Bode plot

An RC low-pass with its corner at 100 Hz, 1 kHz or 10 kHz. Press Sweep and Pip rides a note from 10 Hz to 100 kHz, drawing the gain in decibels as he goes: flat, −3 dB at the corner, then down 20 dB every decade.

Try it yourself: free lesson

“Decibels and Bode plots” is lesson 5 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 25 before it first.

Reading a low-pass

Take an RC low-pass with its corner at fc = 1 ÷ (2π R C):

  • Well below fc: flat at 0 dB, everything passes.
  • At fc: −3 dB, 70.7% of the voltage, half the power.
  • A decade above: about −20 dB, a tenth. Two decades: about −40 dB, a hundredth.

The exact gain is 20 × log10(1 ÷ √(1 + (f ÷ fc)²)). The straight-line sketch, called the asymptotes, bends at fc, which is why it's called the corner frequency.

Reading a high-pass

A high-pass is the mirror image. Example: a microphone's low-cut filter with 1.6 kΩ and 1 µF has its corner near 100 Hz. Rumble at 10 Hz, a decade below, is about −20 dB; voice at 1 kHz is about 0 dB.

−3 dB at fc = 100 Hz+20 dB per decadestraight-line guide1101001k10k0−50−40−30−20−10gain (dB)frequency (Hz)
High-pass: −3 dB at the cutoff, then 20 dB per decade

Stacking stages

Put two stages in a row and their ratios multiply, so on a Bode plot their decibels simply add. Two RC low-passes in a row fall 40 dB per decade once past both corners. An amplifier's flat +20 dB lifts the whole curve by 20 dB. That's why engineers design filters and amplifiers on Bode plots: every stage is just another line to add.

A full Bode plot also shows phase: an RC low-pass lags 45° at its corner and heads for 90° above it.

Free lesson

Now build it yourself

Each lesson comes in three short parts: see the idea, try it on a live board, then build it yourself, with quick checks as you go.

Try it yourself: free lesson

“Decibels and Bode plots” is lesson 5 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 25 before it first.

Or start from the very first lesson, no account needed

Work it out

Practice questions

Three quick questions from the lessons. Pick an answer to check it.

  1. Question 1 of 3An amplifier has a voltage gain of 20. How many decibels is that?
    Show the answer

    Answer: 26 dB. ×20 = ×10 × ×2. Multiplying ratios means adding decibels, so 20 + 6 = 26 dB. Doubling the 20 dB for the ×2 would give 40 dB, which is ×100. A ×2 only adds 6 dB.

    • Why not “20 dB”? 20 dB is a voltage gain of 10, not 20. A gain of 20 is ×10 then ×2, so 20 + 6 dB.
    • Why not “40 dB”? 40 dB is a gain of 100. The extra ×2 only adds 6 dB, not another 20.
  2. Question 2 of 3A gain of 0 dB means the output is…
    Show the answer

    Answer: the same size as the input. A decibel is a ratio. 0 dB is a ratio of 1, the same as the input. Nothing at all would be minus infinity dB, and ten times bigger is +20 dB.

    • Why not “ten times the input”? Ten times the input is +20 dB. 0 dB means a ratio of exactly 1.
    • Why not “zero”? An output of nothing is a ratio of zero, which would be minus infinity dB.
  3. Question 3 of 3A filter's output is half its input. In decibels, that's…
    Show the answer

    Answer: −6 dB. A ratio of 0.5 is −6 dB in the dB table. −3 dB is 70.7%, half the power, and −20 dB is a tenth.

    • Why not “−20 dB”? −20 dB is a tenth of the input, much smaller than a half.
    • Why not “−3 dB”? −3 dB is 70.7% of the voltage, half the power. Half the voltage is −6 dB.
Keep practising: free lesson

“Decibels and Bode plots” is lesson 5 of 6 in Oscillation Coast, Electronics World 4. Free with an account. Lessons unlock in order, so you’ll do the 25 before it first.

Questions people ask

What is a Bode plot?

A graph of a circuit's gain in decibels against frequency, with frequency on a logarithmic axis. Each decade, a step of ten, gets the same width. Bode plots usually come with a second graph of phase against frequency.

What does 20 dB per decade mean?

Each time the frequency goes up ten times, the gain falls by 20 dB, which is a tenth of the voltage. It's the slope of a first-order filter, one resistor and one capacitor, past its corner. That's the same as about 6 dB per doubling.

Why is the corner frequency the −3 dB point?

At the corner, a first-order filter's output is 1 ÷ √2 ≈ 70.7% of its input, which is −3 dB. It's the point where the flat line and the sloping line of the straight-line sketch meet; the real curve passes 3 dB below that corner.

How do I sketch a Bode plot by hand?

Draw a flat line at the pass-band gain up to the corner frequency, then a straight line falling 20 dB per decade for each resistor-capacitor pair. Mark 3 dB below the corner. The real curve rounds the corner and hugs the lines elsewhere.

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