title: Tutorial 105: Analysis Tools¶

Tutorial 105: Analysis Tools¶

Overview¶

Learn to use GeckoCIRCUITS analysis tools for steady-state analysis, frequency response (Bode plots), and small-signal characterization of power converters.

Level: Intermediate (⅔)

Duration: 40-50 minutes

Series: Getting Started

Status: Placeholder - Features may vary by GeckoCIRCUITS version

Learning Objectives¶

By the end of this tutorial, you will: - [ ] Perform steady-state (periodic) analysis - [ ] Generate Bode plots for control loop design - [ ] Measure transfer functions (input-to-output, control-to-output) - [ ] Analyze stability margins (gain margin, phase margin)

Prerequisites¶

• Complete Tutorial 104: Running Simulations
• Understanding of frequency response concepts
• Basic control theory knowledge

Analysis Types¶

1. Transient Analysis (Standard)¶

• Time-domain simulation
• Shows startup, transients, and steady-state
• Most common analysis type

2. Steady-State Analysis¶

• Finds periodic operating point directly
• Skips startup transient
• Faster for efficiency calculations

3. AC (Small-Signal) Analysis¶

• Linearizes circuit around operating point
• Generates frequency response (Bode plots)
• Essential for control loop design

Steady-State Analysis¶

Purpose¶

Find the periodic steady-state without simulating startup: - Efficiency calculations at operating point - Waveform analysis without transients - Faster than long transient simulation

Procedure¶

1. Setup: Define fundamental frequency (switching frequency or line frequency)
2. Run: Solver iterates to find periodic solution
3. Verify: Check that waveforms repeat exactly each period

Example: Buck Converter Efficiency¶

1. Build buck converter circuit
2. Enable steady-state analysis
3. Measure: Pin, Pout, losses
4. Calculate: η = Pout / Pin

AC (Frequency Response) Analysis¶

Theory¶

Linearize non-linear switching converter around operating point:

     ┌─────────────────────┐
d̂ ──►│  Converter          │──► v̂out
     │  (linearized model) │
     └─────────────────────┘

Transfer function: Gvd(s) = v̂out(s) / d̂(s)

Key Transfer Functions¶

Bode Plot Interpretation¶

    Gain (dB)                    Phase (deg)
    │                            │ 0°
 40 ┤                            ├─────────────────
    │ ──────┐                    │         ╲
 20 ┤       │                    │          ╲
    │       ╲                    │           ╲
  0 ┤        ╲─────              ├────────────╲────
    │                            │ -180°      ╲
-20 ┤                            │             ╲
    └────────────────── f        └──────────────── f
         fc (crossover)               PM (phase margin)

Stability Margins¶

Analysis Workflow¶

Step 1: Establish Operating Point¶

1. Run transient simulation to steady state
2. Or use steady-state analysis directly
3. Record DC values: Vout, IL, D

Step 2: Inject Small-Signal Perturbation¶

1. Add small AC component to control signal
2. Frequency: sweep from low to high (e.g., 10 Hz to fs/2)
3. Amplitude: small enough for linear response (1-5%)

Step 3: Measure Response¶

1. Record output AC magnitude and phase
2. At each frequency, calculate:
3. Gain: |Vout_ac| / |d_ac|
4. Phase: ∠Vout - ∠d

Step 4: Plot Results¶

1. Magnitude in dB: 20×log10(|G|)
2. Phase in degrees
3. Identify: crossover, margins, resonances

Buck Converter Example¶

Open-Loop Transfer Function¶

Control-to-output for buck:

Gvd(s) = Vin × (1 + s×RC×C) / [1 + s×L/R + s²×L×C]

Characteristic: - DC gain: Vin - LC resonance: fr = 1/(2π√LC) - ESR zero: fz = 1/(2π×RC×C)

Closed-Loop Design¶

1. Measure open-loop Gvd: Run AC analysis
2. Design compensator: PI, Type II, or Type III
3. Verify loop gain T(s): Gc × Gvd × H
4. Check margins: PM > 45°, GM > 10 dB

Exercises¶

Exercise 1: Steady-State Efficiency¶

1. Build 48V→12V buck converter
2. Run steady-state analysis at full load
3. Calculate efficiency from average powers

Exercise 2: Open-Loop Bode Plot¶

1. Use the buck converter from Exercise 1
2. Perform AC analysis (no feedback)
3. Identify: DC gain, resonance frequency, phase

Exercise 3: Loop Gain with PI Controller¶

1. Add PI compensator to the buck
2. Measure loop gain T(s) = Gc × Gvd
3. Determine phase margin and crossover frequency

Exercise 4: Design for 45° Phase Margin¶

1. Adjust PI gains to achieve PM = 45°
2. Verify with Bode plot
3. Test step response in time domain

Manual AC Analysis Method¶

If automated AC analysis is not available:

Frequency Sweep Procedure¶

1. Set up transient simulation
2. Add sinusoidal perturbation to duty cycle:

   d(t) = D0 + Δd × sin(2πf×t)
   

3. Run simulation for several cycles at frequency f
4. Measure output amplitude and phase
5. Repeat for multiple frequencies (log spacing)
6. Plot magnitude and phase vs. frequency

MATLAB Post-Processing¶

% Load exported data
data = readmatrix('sweep_results.csv');
f = data(:,1);
gain_dB = data(:,2);
phase_deg = data(:,3);

% Bode plot
figure;
subplot(2,1,1);
semilogx(f, gain_dB);
ylabel('Gain (dB)');
grid on;

subplot(2,1,2);
semilogx(f, phase_deg);
ylabel('Phase (deg)');
xlabel('Frequency (Hz)');
grid on;

Common Issues¶

Related Tutorials¶

• 104 - Running Simulations - Basic simulation setup
• 201 - Buck Converter - Test circuit
• 702 - MATLAB Integration - Data export/analysis

References¶

1. Erickson & Maksimovic, Chapter 8: "Converter Transfer Functions"
2. Basso, C. "Switch-Mode Power Supply SPICE Cookbook"
3. Venable, D. "The K Factor: A New Mathematical Tool for Stability Analysis"

Circuit Files¶

Status: Placeholder - buck_ac_analysis.ipes - Buck for frequency analysis - boost_loop_gain.ipes - Boost with compensator - frequency_sweep.ipes - Manual sweep setup

Tutorial Version: 1.0 (Placeholder) Last updated: 2026-02 Compatible with GeckoCIRCUITS v1.0+