Running Palace Simulations¶

import gdsfactory as gf
from ihp import PDK

PDK.activate()

c = gf.components.inductor(
    width=2,
    space=2.1,
    diameter=50,
    turns=1,
    layer_metal="TopMetal2drawing",
    layer_inductor="INDdrawing",
    layer_metal_pin="TopMetal2drawing",
    layers_no_fill=("NoMetFillerdrawing",),
).copy()

# Define guard ring dimensions based on the inductor's bounding box
bbox = c.bbox()
xmin, ymin = bbox.left, bbox.bottom
xmax, ymax = bbox.right, bbox.top

margin_outer = 0.0
margin_inner = -15.0

xlo, xro = xmin - margin_outer, xmax + margin_outer
ybo, yto = ymin - margin_outer, ymax + margin_outer
xli, xri = xmin - margin_inner, xmax + margin_inner
ybi, yti = ymin - margin_inner, ymax + margin_inner

w_v = xli - xlo  # Width vertical walls
h_h = yto - yti  # Height horizontal walls
over = 0.5  # Overlap for Gmsh to fuse the pieces

# Left wall
c.add_ref(
    gf.components.rectangle(
        size=(w_v + over, yto - ybo), layer="Metal1drawing", centered=True
    )
).move((xlo + w_v / 2 + over / 2, (yto + ybo) / 2))
# Right wall
c.add_ref(
    gf.components.rectangle(
        size=(w_v + over, yto - ybo), layer="Metal1drawing", centered=True
    )
).move((xro - w_v / 2 - over / 2, (yto + ybo) / 2))
# Top wall
c.add_ref(
    gf.components.rectangle(
        size=(xro - xlo, h_h + over), layer="Metal1drawing", centered=True
    )
).move(((xro + xlo) / 2, yto - h_h / 2 - over / 2))
# Bottom wall
c.add_ref(
    gf.components.rectangle(
        size=(xro - xlo, h_h + over), layer="Metal1drawing", centered=True
    )
).move(((xro + xlo) / 2, ybo + h_h / 2 + over / 2))

cc = c.copy()

c.draw_ports()
c.plot()

from gsim.palace import DrivenSim

# Create simulation object
sim = DrivenSim()

# Set output directory
sim.set_output_dir("./palace-sim-inductor")

# Set the component geometry
sim.set_geometry(cc)

# Configure layer stack from active PDK
sim.set_stack(substrate_thickness=180.0, include_substrate=True)

# Configure ports
sim.add_port(
    "P1", from_layer="metal1", to_layer="topmetal2", geometry="interlayer", excited=True
)
sim.add_port(
    "P2", from_layer="metal1", to_layer="topmetal2", geometry="interlayer", excited=True
)

# Configure driven simulation (frequency sweep for S-parameters)
sim.set_driven(fmin=10e9, fmax=200e9, num_points=501)

# Validate configuration
print(sim.validate_config())

# Generate mesh (presets: "coarse", "default", "fine")
sim.set_airbox(margin_x=50, margin_y=50, z_above=50, z_below=5)
sim.mesh(preset="default", refined_mesh_size=1.5)

sim.plot_mesh(show_groups=["metal", "P"])

# Run simulation on GDSFactory+ cloud
results = sim.run(check_cache=True)

results.plot_interactive()

results.plot_interactive(phase=True)

import numpy as np
import skrf as rf

f = results.freq * 1e9  # GHz -> Hz
w = 2 * np.pi * f

ports = results.port_names
n = len(ports)

S = np.zeros((len(f), n, n), dtype=complex)
for i, pi in enumerate(ports):
    for j, pj in enumerate(ports):
        S[:, i, j] = results[(pi, pj)].complex

ntwk = rf.Network(f=f, s=S, f_unit="hz")
Z = ntwk.z

Z_sim = Z[:, 0, 0] - Z[:, 0, 1] - Z[:, 1, 0] + Z[:, 1, 1]
f_sim = f

import jax
import jax.numpy as jnp

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


# The RLC impedance function
def z_rlc(w, Q):
    return (1 + 1j * w * Q) / (1 - w**2 + 1j * w / Q)


f_jnp = jnp.array(f_sim, dtype=jnp.float64)
Z_target = jnp.array(Z_sim, dtype=jnp.complex128)


@jax.jit
def loss_fn(param):
    z_fit = param[2] * z_rlc(f_jnp / param[0], param[1])
    z_err = Z_target - z_fit
    return jnp.real(jnp.sum(z_err * jnp.conj(z_err)))

absZ = np.abs(Z_sim)
f0_ini = float(f_sim[np.argmax(absZ)])
R_ini = float(Z_sim.real[0])
mask = absZ > np.max(absZ) / np.sqrt(2)
Q_ini = f0_ini / np.ptp(f_sim[mask]) if mask.sum() > 1 else 5.0
par_ini = jnp.array([f0_ini, Q_ini, R_ini])

print(f"f0 = {f0_ini / 1e9:.3f} GHz | Q = {Q_ini:.3f} | R = {R_ini:.4f} Ohm")

import optax

optimizer = optax.adam(learning_rate=0.05)
opt_state = optimizer.init(par_ini)
vg_fn = jax.jit(jax.value_and_grad(loss_fn))
vg_fn(par_ini)

par = par_ini
for step in range(1000):
    loss, grads = vg_fn(par)
    if step % 200 == 0:
        print(
            f"step {step:4d}: f0={float(par[0]) / 1e9:.4f} GHz  Q={float(par[1]):.3f}  R={float(par[2]):.4f}  loss={float(loss):.3e}"
        )
    updates, opt_state = optimizer.update(grads, opt_state)
    par = optax.apply_updates(par, updates)

f0_fit, Q_fit, R_fit = float(par[0]), float(par[1]), float(par[2])

w0 = 2 * np.pi * f0_fit
tau = Q_fit / w0
L_fit = tau * R_fit
C_fit = 1 / (L_fit * w0**2)

print(f"R = {R_fit:.6f} Ohm")
print(f"L = {L_fit * 1e12:.4f} pH")
print(f"C = {C_fit * 1e15:.4f} fF")
print(f"f0 = {f0_fit / 1e9:.4f} GHz  Q = {Q_fit:.3f}")

import matplotlib.pyplot as plt

print(f"\nR = {R_fit:.6f} Ohm")
print(f"L = {L_fit * 1e12:.4f} pH")
print(f"C = {C_fit * 1e15:.4f} fF")
print(f"f0 = {f0_fit / 1e9:.4f} GHz  Q = {Q_fit:.3f}")

Z_fit = np.array([R_fit * z_rlc(f / f0_fit, Q_fit) for f in f_sim])

fig, axes = plt.subplots(2, 1, figsize=(10, 8))
axes[0].plot(f_sim / 1e9, np.abs(Z_sim), ".", ms=3, label="Sim")
axes[0].plot(
    f_sim / 1e9,
    np.abs(Z_fit),
    label=f"RLC fit  L={L_fit * 1e12:.1f}pH  C={C_fit * 1e15:.1f}fF  R={R_fit:.3f}Ohm",
)
axes[0].set_yscale("log")
axes[0].set_xlabel("f [GHz]")
axes[0].set_ylabel("|Z| [Ohm]")
axes[0].legend()

axes[1].plot(f_sim / 1e9, np.angle(Z_sim, deg=True), ".", ms=3, label="Sim")
axes[1].plot(f_sim / 1e9, np.angle(Z_fit, deg=True), label="RLC fit")
axes[1].set_xlabel("f [GHz]")
axes[1].set_ylabel("arg(Z) [°]")
axes[1].legend()
plt.tight_layout()
plt.show()

from circulax import compile_circuit
from circulax.s_transforms import fdomain_component

# Equivalent circuit:
#
#         --- C ---
#        |         |
# p1 ----+---R--L--+---- p2


@fdomain_component(ports=("p1", "p2"))
def my_inductor(f, R=1.0, L=100e-12, C=10e-15):
    w = 2.0 * jnp.pi * f
    Y_RL = 1.0 / (R + 1j * w * L)  # series RL branch
    Y_C = 1j * w * C  # parallel capacitance
    Y = Y_RL + Y_C
    return jnp.array([[Y, -Y], [-Y, Y]], dtype=jnp.complex128)


net_dict = {
    "instances": {
        "GND": {"component": "ground"},
        "L1": {
            "component": "my_inductor",
            "settings": {"R": R_fit, "L": L_fit, "C": C_fit},
        },
    },
    "ports": {"IN": "L1,p1"},
    "connections": {
        "L1,p2": "GND,p1",
    },
}

models = {"my_inductor": my_inductor, "ground": lambda: 0}

circuit = compile_circuit(net_dict, models)
groups = circuit.groups
freqs = jnp.asarray(f_sim)
Z_target = jnp.asarray(Z_sim)

print("Circuit compiled. System size:", circuit.sys_size)
print("Port map:", circuit.port_map)

from circulax.solvers import setup_ac_sweep
from circulax.utils import update_params_dict

# Port node for IN — check port_map output above
port_node = next(v for k, v in circuit.port_map.items() if k == "IN")


# Positive parametrization
# raw_params -> softplus -> positive physical parameters
def positive(x):
    return jax.nn.softplus(x)


# inverse-softplus
def inv_softplus(y):
    return jnp.log(jnp.exp(y) - 1.0)


def loss_circulax(raw_params):
    params = positive(raw_params)
    R, L, C = params
    g = update_params_dict(groups, "my_inductor", "L1", "R", R)
    g = update_params_dict(g, "my_inductor", "L1", "L", L)
    g = update_params_dict(g, "my_inductor", "L1", "C", C)

    y_op = circuit.with_groups(g)()
    ac = setup_ac_sweep(groups=g, num_vars=circuit.sys_size, port_nodes=[port_node])
    sol = ac(freqs=freqs, y_dc=y_op)

    S11 = sol[:, 0, 0]
    Z_cx = 50.0 * (1 + S11) / (1 - S11)
    err_re = jnp.real(Z_cx) - jnp.real(Z_target)
    err_im = jnp.imag(Z_cx) - jnp.imag(Z_target)
    loss = jnp.mean(err_re**2 + err_im**2)

    return loss


raw_params_ini = inv_softplus(
    jnp.array(
        [
            R_fit,
            L_fit,
            C_fit,
        ]
    )
)

optimizer = optax.adam(1e-2)
opt_state = optimizer.init(raw_params_ini)
vg_fn = jax.jit(jax.value_and_grad(loss_circulax))
vg_fn(raw_params_ini)  # warm-up

raw_params = raw_params_ini
for step in range(500):
    loss, grads = vg_fn(raw_params)
    if step % 20 == 0:
        params = positive(raw_params)
        R_, L_, C_ = params
        print(
            f"step {step:3d}: R={float(R_):.5f} Ohm  L={float(L_) * 1e12:.3f} pH  C={float(C_) * 1e15:.3f} fF  loss={float(loss):.3e}"
        )
    updates, opt_state = optimizer.update(grads, opt_state)
    raw_params = optax.apply_updates(raw_params, updates)

R_fit_cx, L_fit_cx, C_fit_cx = [float(x) for x in positive(raw_params)]
f0_cx = 1.0 / (2 * np.pi * np.sqrt(L_fit_cx * C_fit_cx))
Q_cx = 2 * np.pi * f0_cx * L_fit_cx / R_fit_cx

print(f"\nR = {R_fit_cx:.6f} Ohm")
print(f"L = {L_fit_cx * 1e12:.4f} pH")
print(f"C = {C_fit_cx * 1e15:.4f} fF")
print(f"f0 = {f0_cx / 1e9:.4f} GHz  Q = {Q_cx:.3f}")

g_final = update_params_dict(groups, "my_inductor", "L1", "R", R_fit_cx)
g_final = update_params_dict(g_final, "my_inductor", "L1", "L", L_fit_cx)
g_final = update_params_dict(g_final, "my_inductor", "L1", "C", C_fit_cx)

y_op_final = circuit.with_groups(g_final)()
ac_final = setup_ac_sweep(
    groups=g_final, num_vars=circuit.sys_size, port_nodes=[port_node]
)
sol_final = ac_final(freqs=freqs, y_dc=y_op_final)

S11_final = sol_final[:, 0, 0]
Z_cx_final = 50.0 * (1 + S11_final) / (1 - S11_final)

fig, axes = plt.subplots(2, 1, figsize=(10, 8))
axes[0].plot(f_sim / 1e9, np.abs(Z_sim), ".", ms=3, label="Sim original")
axes[0].plot(
    f_sim / 1e9, np.abs(Z_fit), label=f"Analytical fit  L={L_fit * 1e12:.1f}pH"
)
axes[0].plot(
    f_sim / 1e9, np.abs(Z_cx_final), label=f"Circulax fit  L={L_fit_cx * 1e12:.1f}pH"
)
axes[0].set_yscale("log")
axes[0].set_xlabel("f [GHz]")
axes[0].set_ylabel("|Z| [Ohm]")
axes[0].legend()

axes[1].plot(
    f_sim / 1e9, np.angle(np.array(Z_sim), deg=True), ".", ms=3, label="Sim original"
)
axes[1].plot(f_sim / 1e9, np.angle(np.array(Z_fit), deg=True), label="Analytical fit")
axes[1].plot(
    f_sim / 1e9, np.angle(np.array(Z_cx_final), deg=True), label="Circulax fit"
)
axes[1].set_xlabel("f [GHz]")
axes[1].set_ylabel("arg(Z) [°]")
axes[1].legend()
plt.tight_layout()
plt.show()