Diode Clipper¶

Introduction¶

In this example, we will simulate a classic Diode Clipper (Limiter) circuit. This circuit is a fundamental building block in analog signal processing, used to protect sensitive components from voltage spikes or to shape waveforms by "clipping" signal peaks.

From a simulation perspective, the Diode Clipper serves as a critical benchmark for testing non-linear solvers. As the input voltage crosses the diode's forward-bias threshold, the component's impedance changes rapidly—spanning orders of magnitude from "off" to "on." This behavior creates a stiff system of differential equations, requiring a robust, adaptive step-size controller to maintain numerical stability.

In [1]:

import time

import diffrax
import jax
import jax.numpy as jnp
import matplotlib.pyplot as plt

from circulax.compiler import compile_netlist
from circulax.components.electronic import Diode, Resistor, VoltageSourceAC
from circulax.solvers import analyze_circuit, setup_transient

jax.config.update("jax_enable_x64", True)

import time import diffrax import jax import jax.numpy as jnp import matplotlib.pyplot as plt from circulax.compiler import compile_netlist from circulax.components.electronic import Diode, Resistor, VoltageSourceAC from circulax.solvers import analyze_circuit, setup_transient jax.config.update("jax_enable_x64", True)

Defining the Netlist¶

In [2]:

vpp = 2.0
net_dict = {
    "instances": {
        "GND": {"component": "ground"},
        "Vin": {
            "component": "source_voltage",
            "settings": {
                "V": vpp,
                "freq": 1e3,
            },
        },
        "R1": {"component": "resistor", "settings": {"R": 1000.0}},
        "D1": {
            "component": "diode",
            "settings": {
                "Is": 1e-14,
            },
        },
        "D2": {
            "component": "diode",
            "settings": {
                "Is": 1e-14,
            },
        },
    },
    "connections": {
        "GND,p1": ("Vin,p2", "D1,p2", "D2,p1"),
        "Vin,p1": "R1,p1",
        "R1,p2": ("D1,p1", "D2,p2"),
    },
}

vpp = 2.0 net_dict = { "instances": { "GND": {"component": "ground"}, "Vin": { "component": "source_voltage", "settings": { "V": vpp, "freq": 1e3, }, }, "R1": {"component": "resistor", "settings": {"R": 1000.0}}, "D1": { "component": "diode", "settings": { "Is": 1e-14, }, }, "D2": { "component": "diode", "settings": { "Is": 1e-14, }, }, }, "connections": { "GND,p1": ("Vin,p2", "D1,p2", "D2,p1"), "Vin,p1": "R1,p1", "R1,p2": ("D1,p1", "D2,p2"), }, }

In [4]:

models_map = {
    "resistor": Resistor,
    "diode": Diode,
    "source_voltage": VoltageSourceAC,
    "ground": lambda: 0,
}

print("1. Compiling Circuit...")
groups, num_vars, port_map = compile_netlist(net_dict, models_map)
print(f"   System Size: {num_vars} variables")
print(f"   Port Map: {port_map}")


print("2. Initializing Solver Strategy...")
linear_strat = analyze_circuit(groups=groups, num_vars=num_vars, backend="klu_split")

print("3. Solving DC Operating Point...")
y_guess = jnp.zeros(num_vars)
y_dc = linear_strat.solve_dc(groups, y_guess)
print(f"   DC Solution (First 5): {y_dc[:5]}")

print("4. Running Transient Simulation...")


transient_sim = setup_transient(groups, linear_strategy=linear_strat)

t_max = 2e-3
saveat = diffrax.SaveAt(ts=jnp.linspace(0, t_max, 300))

step_controller = diffrax.PIDController(
    rtol=1e-3,
    atol=1e-6,
    pcoeff=0.2,
    icoeff=0.5,
    dcoeff=0.4,
    force_dtmin=True,
    dtmin=1e-8,
    dtmax=1e-5,
    error_order=2,
)

start = time.time()
sol = transient_sim(
    t0=0,
    t1=t_max,
    dt0=1e-6 * t_max,
    y0=y_dc,
    saveat=saveat,
    stepsize_controller=step_controller,
)
stop = time.time()

if sol.result == diffrax.RESULTS.successful:
    print("   ✅ Simulation Successful")
    print(
        f"Performed {sol.stats['num_steps']} steps performed in {stop - start:.2f} seconds"
    )
    ts = sol.ts
    v_in = sol.ys[:, port_map["Vin,p1"]]
    v_out = sol.ys[:, port_map["R1,p2"]]

    plt.figure(figsize=(8, 4))
    plt.plot(ts * 1000, v_in, "k--", alpha=0.5, label=f"Input ({vpp} V Sine)")
    plt.plot(ts * 1000, v_out, "r-", linewidth=2, label="Output (Clipped)")
    plt.title("Diode Limiter: Hard Non-Linearity Test")
    plt.xlabel("Time (ms)")
    plt.ylabel("Voltage (V)")
    plt.legend()
    plt.grid(True)
    plt.show()
else:
    print("   ❌ Simulation Failed")
    print(f"   Result Code: {sol.result}")

models_map = { "resistor": Resistor, "diode": Diode, "source_voltage": VoltageSourceAC, "ground": lambda: 0, } print("1. Compiling Circuit...") groups, num_vars, port_map = compile_netlist(net_dict, models_map) print(f" System Size: {num_vars} variables") print(f" Port Map: {port_map}") print("2. Initializing Solver Strategy...") linear_strat = analyze_circuit(groups=groups, num_vars=num_vars, backend="klu_split") print("3. Solving DC Operating Point...") y_guess = jnp.zeros(num_vars) y_dc = linear_strat.solve_dc(groups, y_guess) print(f" DC Solution (First 5): {y_dc[:5]}") print("4. Running Transient Simulation...") transient_sim = setup_transient(groups, linear_strategy=linear_strat) t_max = 2e-3 saveat = diffrax.SaveAt(ts=jnp.linspace(0, t_max, 300)) step_controller = diffrax.PIDController( rtol=1e-3, atol=1e-6, pcoeff=0.2, icoeff=0.5, dcoeff=0.4, force_dtmin=True, dtmin=1e-8, dtmax=1e-5, error_order=2, ) start = time.time() sol = transient_sim( t0=0, t1=t_max, dt0=1e-6 * t_max, y0=y_dc, saveat=saveat, stepsize_controller=step_controller, ) stop = time.time() if sol.result == diffrax.RESULTS.successful: print(" ✅ Simulation Successful") print( f"Performed {sol.stats['num_steps']} steps performed in {stop - start:.2f} seconds" ) ts = sol.ts v_in = sol.ys[:, port_map["Vin,p1"]] v_out = sol.ys[:, port_map["R1,p2"]] plt.figure(figsize=(8, 4)) plt.plot(ts * 1000, v_in, "k--", alpha=0.5, label=f"Input ({vpp} V Sine)") plt.plot(ts * 1000, v_out, "r-", linewidth=2, label="Output (Clipped)") plt.title("Diode Limiter: Hard Non-Linearity Test") plt.xlabel("Time (ms)") plt.ylabel("Voltage (V)") plt.legend() plt.grid(True) plt.show() else: print(" ❌ Simulation Failed") print(f" Result Code: {sol.result}")

1. Compiling Circuit...

   System Size: 4 variables
   Port Map: {'D2,p2': 1, 'D1,p1': 1, 'R1,p2': 1, 'D1,p2': 0, 'D2,p1': 0, 'GND,p1': 0, 'Vin,p2': 0, 'Vin,p1': 2, 'R1,p1': 2}
2. Initializing Solver Strategy...
3. Solving DC Operating Point...

   DC Solution (First 5): [0. 0. 0. 0.]
4. Running Transient Simulation...

   ✅ Simulation Successful
Performed 591 steps performed in 1.23 seconds

In [ ]: