CSCM 373-01 — Fuzzbox Physics — CalArts

Reading
Schematics

Symbols, passive components & RC filters

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Why Bother?

Schematics Are the Sheet Music of Electronics

Passive = no external power needed. The component shapes the signal using only the energy already in it.

Passive Components

The Big Three

Resistor
Resists current flow. Measured in ohms (Ω). Converts electrical energy to heat.
Capacitor
Stores charge. Blocks DC, passes AC. Measured in farads (F). Key to every filter.
Inductor
Stores energy in a magnetic field. Passes DC, resists AC changes. Measured in henrys (H).
Resistor

The Resistor — Opposition to Flow

  • Unit: ohm (Ω). Common guitar-circuit values: 1 kΩ – 1 MΩ
  • Analogy: a narrow section of pipe — restricts flow, creates a pressure drop
  • In audio: sets gain, biases transistors, creates voltage dividers
  • Schematic shorthand: 22k = 22,000 Ω   1M = 1,000,000 Ω

The zigzag symbol is IEEE (US). The rectangle is IEC (international). You'll see both.

IEEE (US) R = 22 kΩ IEC (INTERNATIONAL)
Capacitor

The Capacitor — Frequency-Dependent

  • Unit: farad (F). Audio circuits use nF and pF (tiny!)
  • Key idea: a capacitor's impedance decreases as frequency goes up
  • Low freq: high impedance → blocks the signal
  • High freq: low impedance → passes the signal
  • Analogy: a spring-loaded gate that opens wider the faster you push

103 = 10 nF. Ceramic cap codes: first two digits are significant, third is the multiplier (number of zeros), result in picofarads.

UNPOLARIZED C = 10 nF POLARIZED (ELECTROLYTIC) +
Reading Schematics

Other Symbols You'll See

Ground
0V reference point
Junction
Wires are connected
Crossing
Wires NOT connected
Potentiometer
Variable resistor (knob)

Tip: Schematics read left-to-right like a sentence. Signal enters on the left, exits on the right. Power rails run along the top, ground along the bottom.

Key Concept

Capacitors Care About Frequency

A resistor has the same resistance at any frequency. A capacitor does not.

ZC = 1 / (2πfC)
ZC = impedance (ohms)  •  f = frequency (Hz)  •  C = capacitance (farads)
Frequency Capacitor Impedance Result
Low (bass) HIGH — cap acts like an open circuit Signal is blocked
High (treble) LOW — cap acts like a short circuit Signal passes through

This is the whole secret of passive filters: put a capacitor in the right place and it will sort frequencies for you.

Building Block

The Voltage Divider

Two components in series form a voltage divider. The output voltage depends on the ratio of their impedances.

Vout = Vin × Z2 / (Z1 + Z2)
  • If Z2 is small compared to Z1, output is low
  • If Z2 is large compared to Z1, output is high

Now replace one of the resistors with a capacitor and the division becomes frequency-dependent.

V_in Z₁ V_out Z₂
RC Filter #1

Low-Pass Filter — Treble Cut

R on top, C on bottom.

  • At low frequencies: cap impedance is high → Vout is high → bass passes
  • At high frequencies: cap impedance drops → signal is shunted to ground → treble is cut
fc = 1 / (2πRC)

With R = 22 kΩ and C = 10 nF:

fc = 1 / (2π × 22000 × 0.00000001) ≈ 723 Hz

This is your guitar's tone knob! Frequencies above ~723 Hz get progressively quieter.

IN R 22 kΩ OUT C 10 nF LOW-PASS (TREBLE CUT)
RC Filter #2

High-Pass Filter — Bass Cut

C on top, R on bottom. Just swap the positions!

  • At low frequencies: cap impedance is high → blocks the signal → bass is cut
  • At high frequencies: cap impedance drops → signal passes through → treble passes
fc = 1 / (2πRC)   (same formula!)

Same R and C → same cutoff frequency, but now everything below 723 Hz gets quieter.

IN C 10 nF OUT R 22 kΩ HIGH-PASS (BASS CUT)
Comparison

Same Parts, Different Arrangement

Filter Series Element Shunt Element What Passes
Low-Pass Resistor (R in series) Capacitor (C to ground) Frequencies below fc
High-Pass Capacitor (C in series) Resistor (R to ground) Frequencies above fc

The tone knob on a guitar is literally a low-pass filter: a pot (variable R) in series with a cap to ground. Turn it down → lower R → lower cutoff → darker sound.

Coupling caps in pedals are high-pass filters: a cap in series blocks DC (0 Hz) and lets audio pass. The R is the input impedance of the next stage.

Hands-On

Today's Simulation Tools

1. CircuitCanvas
Draw schematics from symbols. No simulation — just layout practice. Start here to learn to read and draw circuits.
circuitcanvas.com
2. EveryCircuit
Animated simulation. Watch current flow and voltage levels change in real time. Great for intuition.
everycircuit.com
3. Falstad
Full simulation with oscilloscope views. Closest to real lab instruments. Build and probe any circuit.
falstad.com/circuit

Progression: draw the schematic → simulate it → build it on a breadboard

Next Steps

Worksheet Time

Goal: By the end of today you should be able to look at any RC circuit and immediately say whether it's a low-pass or high-pass filter, and estimate its cutoff frequency.

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