AC Small Signal Analysis

AC Small Signal Analysis #

AC Small Signal Analysis (also known as AC Analysis or Frequency Response Analysis) determines how your circuit responds to different frequencies. Essential for designing filters, amplifiers, and understanding frequency-dependent behavior.

What It Does #

AC analysis:

  1. Calculates the DC operating point first
  2. Linearizes all components around that point
  3. Applies a small AC signal at various frequencies
  4. Measures magnitude and phase response

When to Use #

Use AC Small Signal Analysis for:

  • Filter Design: Low-pass, high-pass, band-pass, notch filters
  • Amplifier Response: Bandwidth, gain vs. frequency
  • Stability Analysis: Phase margin, gain margin
  • Impedance Analysis: Input/output impedance vs. frequency
  • Resonant Circuits: Q factor, resonant frequency

Configuration Parameters #

Frequency Range #

  • Start Frequency: Lowest frequency to analyze (e.g., 1 Hz)
  • Stop Frequency: Highest frequency to analyze (e.g., 1 MHz)
  • Points per Decade: Resolution of frequency sweep

Sweep Types #

  • Decade: Logarithmic sweep (10x per step)
  • Octave: Logarithmic sweep (2x per step)
  • Linear: Equal frequency steps

AC Source Setup #

Your circuit must have at least one AC source:

V1 in 0 DC 5 AC 1

The “AC 1” specifies a 1V test signal for analysis.

Understanding Results #

Magnitude Plot (Bode Plot) #

  • Y-axis: Gain in dB (20×log₁₀(Vout/Vin))
  • X-axis: Frequency (usually logarithmic)
  • Key Points:
    • 0 dB = Unity gain
    • -3 dB = Half power point (cutoff frequency)
    • -20 dB/decade = First-order rolloff
    • -40 dB/decade = Second-order rolloff

Phase Plot #

  • Y-axis: Phase shift in degrees
  • X-axis: Frequency (logarithmic)
  • Key Points:
    • 0° = No phase shift
    • -45° = First-order system at cutoff
    • -90° = Quarter cycle delay
    • -180° = Inversion (check stability!)

Common Circuit Examples #

RC Low-Pass Filter #

* Simple RC low-pass
V1 in 0 DC 0 AC 1
R1 in out 1k
C1 out 0 1u
.ac dec 10 0.1 100k
  • Cutoff frequency: fc = 1/(2πRC) = 159 Hz
  • -3dB at 159 Hz
  • -20dB/decade rolloff

LC Tank Circuit #

* Parallel LC resonant circuit
I1 0 tank DC 0 AC 1m
L1 tank 0 1m
C1 tank 0 1n
R1 tank 0 10k
.ac dec 100 1k 1meg
  • Resonant frequency: f₀ = 1/(2π√LC) = 159 kHz
  • Peak impedance at resonance
  • Q factor = R√(C/L)

Op-Amp Active Filter #

* Second-order Butterworth low-pass
V1 in 0 DC 0 AC 1
X1 in 0 n1 vcc vee OPAMP
R1 in n1 10k
R2 n1 out 10k
C1 n1 0 100n
C2 out n1 100n
R3 out 0 10k
  • Cutoff: 159 Hz
  • -40dB/decade rolloff
  • Butterworth response (maximally flat)

Analysis Tips #

Setting Up Your Circuit #

  1. DC Bias First: Ensure proper DC operating point
  2. AC Source: Add “AC 1” to input source
  3. Small Signal: AC analysis assumes linear operation
  4. Multiple Sources: Only one AC source at a time

Interpreting Results #

  1. Gain Margin: How much gain before instability

    • Look for 0dB crossing when phase = -180°
    • Should be > 6dB for stability

  2. Phase Margin: How much phase shift before instability

    • Look for phase when gain = 0dB
    • Should be > 45° for good stability

  3. Bandwidth: Frequency range with useful gain

    • Usually measured at -3dB points
    • Gain-bandwidth product for op-amps

  4. Resonances: Peaks in frequency response

    • Can cause ringing or oscillation
    • Check Q factor isn’t too high

Advanced Features (Premium) #

Monte Carlo AC Analysis #

Analyze frequency response with component tolerances:

  • Shows response spread due to variations
  • Identifies worst-case scenarios
  • Essential for production design

Temperature Sweep #

See how frequency response changes with temperature:

  • Capacitor values drift
  • Transistor parameters shift
  • Critical for precision circuits

Troubleshooting #

No AC Response #

  • Check AC source specification
  • Verify DC operating point is correct
  • Ensure probes are placed correctly

Unexpected Results #

  • Components may be saturated (nonlinear)
  • Check for numerical issues at extremes
  • Verify component values and connections

Convergence Issues #

  • Simplify circuit first
  • Check DC operating point
  • Add small resistances to isolated nodes

Export Options #

Premium users can export:

  • CSV data for external plotting
  • Magnitude and phase data
  • Complex impedance values
  • Multi-probe datasets

See Also #