Electrical & Electronics Engineering / Bode & Nyquist Stability
FREE TO EXPLORE
LABORATORY 48 · ELECTRICAL & ELECTRONICS ENGINEERING

Frequency Response Analysis: Bode Magnitude/Phase Plots and Nyquist Stability Criterion

Measure open-loop frequency response of a linear dynamical control system, constructing experimental Bode plots, identifying gain margin (GM) and phase margin (PM), and evaluating stability via Nyquist encirclements. Explore interactive circuit analysis, electronics simulation, and electrical engineering telemetry.

CIRCUIT ANALYSIS · ANALOG · DIGITAL · MACHINES · POWER SYSTEMS · CONTROL & INSTRUMENTATION

Your virtual electrical & electronics engineering laboratory.

HIGH-FREQUENCY ASYMPTOTIC MAGNITUDE—
INSTRUMENTATION TELEMETRY

Ready to sample with Log Frequency = 1.0 decade.

1.0 decade
Calibrated Dynamic Signal Analyzer & Configurable Analog Plant baseline operating point stabilized at 25.0 °C

Adjust Log Frequency, then execute electrical instrumentation acquisition.

Electrical telemetry is sampled with calibrated high-precision instruments using 64-bit IEEE 754 precision buffers. Residuals reflect ordinary least-squares regression across successive observations. Continuous data structures support high-fidelity circuit and power system modeling.

Electrical engineering assumptions and boundary limits

Assumes ideal linear operating conditions without thermal breakdown or non-linear core saturation Calibrated using the Dynamic Signal Analyzer & Configurable Analog Plant under controlled temperature and 64-bit IEEE 754 precision instrumentation buffers. Ordinary least-squares regression yields R² > 0.99999.

Laboratory apparatus & testing equipment.

Bode & Nyquist Stability Precision Workstation

Provides regulated excitation, calibrated terminal access, and low-parasitic interconnects for cauchy argument principle, nyquist critical point (-1 + j0) & closed-loop stability.

True-RMS Digital Multimeter (6.5-digit Keysight / Fluke)

Measures terminal voltages, branch currents, and precision DC/AC parameters with ±0.0035% baseline accuracy.

Dual-Channel Digital Storage Oscilloscope (100 MHz, 1 GSa/s)

Captures time-domain waveforms, phase shifts, transient dynamics, and harmonic spectra for bode & nyquist stability.

Regulated Linear DC / AC Variable Power Source

Supplies low-noise, ripple-free voltage and current excitation with adjustable current limiting.

Calibrated Decade Resistance & Component Substitution Box

Provides precision 0.1% tolerance standard passive values to establish calibrated log frequency conditions.

Four-Terminal Kelvin Lead Wire & BNC Coaxial Cable Set

Minimizes lead resistance, inductive pickup, and ambient EMI interference across all test ports.

FOLLOW THE METHOD

A reason behind every step.

Measure open-loop frequency response of a linear dynamical control system, constructing experimental Bode plots, identifying gain margin (GM) and phase margin (PM), and evaluating stability via Nyquist encirclements. Standardized parameter settings: 0.2, 0.5, 0.8, 1.1, 1.4, 1.7 decade.

  1. Visual Inspection & Pre-Flight Zero Tare: Inspect all circuit connections, breadboard jumpers, and terminal blocks. Verify that instrument ground planes are tied to earth and execute zero tare on all digital meters.
  2. Excitation Source & Baseline Calibration: Energize the regulated supply, set baseline operating thresholds, and calibrate the log frequency using the precision standard reference meter.
  3. Systematic Parameter Variation & Settling: Increment the log frequency systematically across the designated experimental range (0.2 to 1.7 decade), permitting thermal settling at each setpoint.
  4. Multi-Meter & Oscilloscope Waveform Acquisition: Record the primary output metric (High-Frequency Asymptotic Magnitude) alongside auxiliary telemetry. Verify waveform symmetry, DC offset, and harmonic integrity on the oscilloscope.
  5. Cross-Validation & Redundant Trial Verification: Execute repeated forward and reverse sweeps to detect hysteresis, thermal drift, or non-linear saturation effects across the device under test (DUT).
  6. Shutdown, De-energization & Data Archival: Reduce source excitation smoothly to zero, de-energize all primary supplies, discharge residual capacitive elements, and export raw telemetry to the data buffer.
YOUR NOTEBOOK · 0 OBSERVATIONS

Turn measurements into electrical engineering insight.

See a complete example report ↗

Points are your recorded observations. The solid regression line validates Bode & Nyquist Stability mathematical scaling.

LINEAR REGRESSION FIT · y = mx + b
Magnitude = -20.0000 · log₁₀(ω/ω_c)
#Log Normalized Frequency log₁₀(ω/ω_c) (decade)High-Frequency Asymptotic Magnitude (dB)Log normalized frequency decade log₁₀(ω/ω_c)Asymptotic magnitude (dB)

No readings yet. Execute an electrical trial and record it.

CHECK YOUR UNDERSTANDING

Explain what the circuit metrics mean.

Question 1: In the study of Bode & Nyquist Stability, the primary dependent variable measured is:

Question 2: The mathematical relationship governing Bode & Nyquist Stability is modeled as:

Question 3: The target benchmark parameter derived from regression analysis is:

Question 4: Which instrumentation technique effectively eliminates lead wire resistance error?

THEORY AND ELECTROMAGNETIC CONTEXT

Electrical engineering background & physical principles.

The experimental analysis of frequency response analysis: bode magnitude/phase plots and nyquist stability criterion investigates the electrotechnical behavior of dynamic signal analyzer & configurable analog plant. This university laboratory module focuses on cauchy argument principle, nyquist critical point (-1 + j0) & closed-loop stability, establishing accurate mathematical transfer characteristics across standard operational domains.

Magnitude = -20.0000 · log₁₀(ω/ω_c)

Calibrated using the Dynamic Signal Analyzer & Configurable Analog Plant under controlled temperature and 64-bit IEEE 754 precision instrumentation buffers. Ordinary least-squares regression yields R² > 0.99999.