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Comparator relaxation oscillator

See how capacitor charging and comparator hysteresis produce a square wave.

Analog

Use Transient to inspect the ramp, hysteresis thresholds, and switched output.

Editor showing the Comparator relaxation oscillator SPICE example as an unsaved schematic.
Comparator relaxation oscillator opens as an editable, unsaved schematic.

Open and run

  1. Open Examples from the Home ribbon.
  2. Choose Comparator relaxation oscillator.
  3. Open Simulate and choose Setup to review the analyses.
  4. Choose Run for one analysis or Run All for the complete configured set.
  5. Select a matching Scope view after the run. Use Save as sheet to keep the example or Discard to close it.

Sheets, analyses, and Scope

Comparator relaxation oscillator

#

Setup: Transient oscillation

AnalysisConfiguration
Transient
  • Step 5u
  • Stop 8m
  • Initial conditions Enabled

Scope views and expected results

Ramp, threshold, and output

Analysis: Transient

Waveforms
  • V(ramp)
  • V(thresh)
  • V(out)
Readouts
  • Output swingPk-PkV(out)
  • Lower thresholdMinV(ramp)
  • Upper thresholdMaxV(ramp)

Python scripts

These scripts are included with the example. Review trusted project code before choosing Run.

Set oscillator frequency.py

Default sheet: Comparator relaxation oscillator

target_hz = 1000
capacitance_f = 100e-9

import math

if target_hz <= 0 or capacitance_f <= 0:
    raise ValueError("Frequency and capacitance must be positive")

# Equal 100k bias and feedback resistors; the divider adds 50k to R3.
resistance = 100e3
bias_resistance = resistance + resistance / 2
beta = bias_resistance / (bias_resistance + resistance)
# For this symmetric ideal comparator: T = 2*R4*C1*ln((1+beta)/(1-beta)).
timing_resistance = 1 / (2 * target_hz * capacitance_f * math.log((1 + beta) / (1 - beta)))
sheet = get_sheet("Comparator relaxation oscillator").override(
    R1=resistance, R2=resistance, R3=resistance, R5=resistance,
    R4=timing_resistance, C1=capacitance_f,
)
print(f"Target: {target_hz:g} Hz; R4={timing_resistance / 1000:.3f} kohm; C1={capacitance_f * 1e9:g} nF")

result = sheet.tran(8 / target_hz, step=1 / (200 * target_hz),
                    max_step=1 / (200 * target_hz), uic=True,
                    save=["V(out)", "V(ramp)", "V(thresh)"])
output = result.v("out").window(start=2 / target_hz)
crossings = output.crossings((output.min() + output.max()) / 2, edge="rising")
if len(crossings) < 2:
    raise ValueError("No steady oscillation found; try a lower target frequency")
measured_hz = (len(crossings) - 1) / (crossings[-1] - crossings[0])
print(f"Measured: {measured_hz:.1f} Hz")

fig, ax = subplots(1, 1, title="Oscillator frequency design")
ax.set(xlabel="Time", xformat="time", ylabel="Voltage (V)")
for node in ["out", "ramp", "thresh"]:
    ax.plot(result.v(node), label=node)
fig.show()
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