SYCAN terminology reference

A glossary of every short symbol, abbreviation and parameter name that appears across SYCAN’s component models, analyses and noise machinery. Symbols are grouped by topic; each entry lists the source code spelling followed by the fully-expanded mathematical form.

Conventions:

• V_T is the thermal voltage (kT/q), not the threshold voltage. The threshold is V_TH. Mixing these up is the single most common hazard in this codebase.

• mu_n is the in-code spelling of the channel-carrier mobility μ; for PMOS it physically corresponds to μₚ but the same field name is used.

• pol is +1 for NMOS / NPN and −1 for PMOS / PNP. All polarity- aware models compute *_eff = pol · (terminal voltage) so the code can be written once for both polarities.

• All currents use the SPICE sign convention: positive flowing into the named terminal.

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1. Physical constants

Symbol	Code	Meaning	Typical value
k_B	k_B	Boltzmann constant	1.380649 × 10⁻²³ J/K
T	T	Absolute temperature	300 K (≈27 °C)
q	q	Elementary charge	1.602176634 × 10⁻¹⁹ C
V_T	V_T	Thermal voltage k_B · T / q	≈25.85 mV at 300 K

The default _DEFAULT_VT = sp.Rational(2585, 100000) baked into the BJT, diode and sub-threshold MOSFET models is exactly this 25.85 mV value (sp here is sycan.cas). k_B, T, q are exposed as CAS Symbols in sycan.mna so users can substitute numeric values when evaluating noise PSDs.

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2. MOSFET parameters

2.1 Geometry & process

Code	Expanded name	Definition / units
W	Channel width	Drawn gate width [m].
L	Channel length	Drawn gate length [m].
Cox	Oxide capacitance per unit area	C_ox = ε_ox / t_ox [F/m²]. Gate-oxide specific capacitance.
mu_n	Channel-carrier mobility	μₙ for NMOS, μₚ for PMOS [m²/(V·s)]. Same field name used for both polarities.
β	Transconductance parameter (derived)	β = μ · Cox · (W / L) [A/V²]. Computed internally as _beta.

Cox is “C-oxide”, not a capacitor named “Cox”. It is the gate-oxide capacitance per unit gate area, not a total capacitance — multiply by W · L to get the absolute oxide capacitance of one device.

2.2 Threshold & body effect

Code	Expanded name	Definition
V_TH	Threshold voltage (positive magnitude)	Gate-source bias at the strong-inversion boundary. Stored as a positive number for both NMOS and PMOS.
V_TH0	Zero-bias threshold voltage	V_TH evaluated at V_SB = 0. Used in 4T as the parameter; the body-effect term shifts it.
γ	Body-effect coefficient gamma	√V. V_TH(V_SB) = V_TH0 + γ · (√(2 φ_F + V_SB) − √(2 φ_F)). Zero by default → bulk pin is cosmetic.
2 φ_F	Surface potential at strong inversion (phi)	Default ≈ 0.7 V. φ_F is the Fermi potential of the bulk; the surface needs to bend by 2 φ_F for strong inversion.
V_SB	Source-to-bulk voltage	V_SB = V(source) − V(bulk), polarity-flipped internally so V_SB ≥ 0 in physical operation.

In the 3T wrappers (NMOS_3T, PMOS_3T) the bulk is tied to the source, which forces V_SB = 0 — the body-effect term vanishes and V_TH is just V_TH0.

2.3 Channel-length modulation & operating-region model

Code	Expanded name	Definition
λ	Channel-length modulation parameter lam	1/V. Saturation current carries the factor (1 + λ · V_DS_eff); λ = 0 reproduces ideal long-channel.
V_ov	Overdrive voltage	V_ov = V_GS_eff − V_TH. Often called V_GS − V_TH in textbooks.
m	Sub-threshold slope factor	m = 1 + C_d / C_ox. Default 1.5. Controls how steeply weak-inversion current rolls off with V_GS.
V_off	Strong/weak split point (segmented model)	V_off = V_TH + 2 · m · V_T. Boundary between weak and strong inversion in the segmented MOSFET_3T/4T.
I_off	Boundary drain current	I_off = 2 · β · (m · V_T)². The drain current at V_GS_eff = V_off; ensures C¹-smooth join.

2.4 Effective terminal voltages

Code	Definition
V_GS	V(gate)   − V(source) (un-polarised)
V_DS	V(drain)  − V(source) (un-polarised)
V_BS	V(bulk)   − V(source) (un-polarised)
V_GS_eff	pol · V_GS — pol = +1 (NMOS) / −1 (PMOS)
V_DS_eff	pol · V_DS
V_SB_eff	−pol · V_BS (so V_SB ≥ 0 physically)

2.5 Drain-current expressions

Strong-inversion saturation (Shichman-Hodges Level 1, with channel- length modulation):

I_D_mag = (1/2) · μ · Cox · (W/L) · (V_GS_eff − V_TH)² · (1 + λ · V_DS_eff)
I_D     = pol · I_D_mag

Strong-inversion triode:

I_D_mag = β · (V_ov · V_DS_eff − (1/2) · V_DS_eff²) · (1 + λ · V_DS_eff)

Weak inversion (sub-threshold, MOSFET_subthreshold):

I_D_mag = μ · Cox · (W/L) · V_T²
          · exp((V_GS_eff − m · V_TH) / (m · V_T))
          · (1 − exp(−V_DS_eff / V_T))

Weak inversion (segmented 3T/4T form, joined to L1 at V_off):

I_D_mag = I_off · exp((V_GS_eff − V_off) / (m · V_T))
          · (1 − exp(−V_DS_eff / V_T))
          · (1 + λ · V_DS_eff)

2.6 Operating regions

Reported by operating_region():

Region	L1 condition	3T/4T condition
cutoff	V_GS_eff ≤ V_TH	(replaced by weak_inversion in 3T/4T)
weak_inversion	—	V_GS_eff < V_off
triode	V_GS_eff > V_TH, V_DS_eff < V_GS_eff−V_TH	V_GS_eff ≥ V_off, V_DS_eff < V_GS_eff−V_TH
saturation	V_GS_eff > V_TH, V_DS_eff ≥ V_GS_eff−V_TH	V_GS_eff ≥ V_off, V_DS_eff ≥ V_GS_eff−V_TH

2.7 Small-signal MOSFET parameters

Code	Expanded name	Definition (evaluated at (V_GS_op, V_DS_op, V_BS_op))
g_m	Gate transconductance	∂I_D/∂V_GS at the operating point.
g_ds	Drain output conductance	∂I_D/∂V_DS at the operating point. Inverse r_ds = 1/g_ds.
g_mb	Bulk transconductance	∂I_D/∂V_BS at the operating point. Captures back-gate effect.
C_gs	Gate-source capacitance	Intrinsic; stamped as admittance s · C_gs in AC.
C_gd	Gate-drain capacitance	Intrinsic; stamped as admittance s · C_gd in AC. Miller path.

V_GS_op, V_DS_op, V_BS_op are the symbolic operating-point voltages — substitute concrete numbers (or DC-solve outputs) before evaluating an AC response.

2.8 Flicker (1/f) noise parameters

Supported by MOSFET_L1, MOSFET_3T, MOSFET_4T, and MOSFET_subthreshold when include_noise contains "flicker".

Code	Expanded name	Definition
KF	Flicker noise coefficient	Magnitude of the 1/f drain-current PSD. Default 0.
AF	Drain-current exponent	Dimensionless. Default 1.
EF	Frequency exponent	Dimensionless. Default 1 (pure 1/f); 2 → 1/f² roll-off.

PSD form: S_I_D(f) = KF · I_op^AF / freq^EF. The freq symbol is the shared analysis-frequency symbol exposed from sycan.mna.

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3. BJT (Gummel-Poon) parameters

3.1 Junction voltages and ideal transport currents

Code	Expanded name	Definition
V_BE	Base-emitter voltage	V_BE = pol · (V(base) − V(emitter))
V_BC	Base-collector voltage	V_BC = pol · (V(base) − V(collector))
I_BF	Forward ideal transport current	I_BF = IS · (exp(V_BE / (NF · V_T)) − 1)
I_BR	Reverse ideal transport current	I_BR = IS · (exp(V_BC / (NR · V_T)) − 1)
I_CE	Collector-emitter transport current	I_CE = (I_BF − I_BR) / q_B

pol = +1 for NPN, −1 for PNP.

3.2 Model parameters

Code	Expanded name	Default (Ebers-Moll fall-back)
IS	Saturation current	(must be supplied)
BF	Forward current gain (β_F)	(must be supplied)
BR	Reverse current gain (β_R)	(must be supplied)
NF	Forward emission coefficient (ideality factor of B–E ideal diode)	1
NR	Reverse emission coefficient (ideality factor of B–C ideal diode)	1
VAF	Forward Early voltage	∞ (no Early effect)
VAR	Reverse Early voltage	∞
IKF	Forward knee current (high-level injection roll-off)	∞ (no roll-off)
IKR	Reverse knee current	∞
ISE	B–E leakage saturation current (non-ideal recombination diode)	0
NE	B–E leakage emission coefficient	1.5
ISC	B–C leakage saturation current	0
NC	B–C leakage emission coefficient	2

3.3 Base-charge factor

Code	Definition
q_1	1 / (1 − V_BC/VAF − V_BE/VAR). Early-effect term.
q_2	I_BF/IKF + I_BR/IKR. High-level injection term.
q_B	(q_1 / 2) · (1 + sqrt(1 + 4 · q_2)). Normalised majority base charge.

Terminal currents (positive into each terminal):

I_C = pol · (I_CE − I_BC_total)
I_B = pol · (I_BE_total + I_BC_total)
I_E = −(I_C + I_B)

where I_BE_total = I_BF/BF + ISE·(exp(V_BE/(NE·V_T)) − 1) and I_BC_total = I_BR/BR + ISC·(exp(V_BC/(NC·V_T)) − 1).

3.4 Small-signal hybrid-π AC parameters

Linearised around (I_C_op, I_B_op). I_C_op / I_B_op default to per-instance symbols I_C_op_<name> / I_B_op_<name> — pass numeric values (or DC-solve outputs) before evaluating an AC response.

Code	Expanded name	Definition
g_m	Transconductance	g_m = I_C_op / (NF · V_T).
r_pi	Base–emitter resistance	r_pi = BF / g_m. Stamped as conductance 1/r_pi.
r_o	Output resistance	r_o = VAF / I_C_op. Omitted when VAF = ∞.
C_pi	Base–emitter capacitance	Diffusion + B–E depletion. Stamped as admittance s · C_pi.
C_mu	Base–collector capacitance	B–C depletion (Miller path). Stamped as admittance s · C_mu.

3.5 Noise parameters

Code	Source	PSD
shot (C–E)	2 · q · I_C_op	Collector-current shot noise.
shot (B–E)	2 · q · I_B_op	Base-current shot noise.
KF, AF	flicker (B–E)	KF · I_B_op^AF / freq. Enabled when include_noise lists "flicker" and KF != 0.

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4. Diode (Shockley)

4.1 DC and stamping

Code	Expanded name	Definition
IS	Reverse-saturation current	A.
N	Ideality / emission coefficient	Dimensionless; default 1.
V_D	Diode voltage	V_D = V(anode) − V(cathode)
I_D	Diode current (anode → cathode)	I_D = IS · (exp(V_D / (N · V_T)) − 1)
I_op	Operating-point current (for shot noise PSD)	A. Pass a value or use the auto-symbol.

4.2 Small-signal AC

Code	Expanded name	Definition
V_D_op	Operating-point diode bias	Defaults to per-instance symbol V_D_op_<name> if not supplied.
g_d	Small-signal conductance	g_d = ∂I_D/∂V_D = (IS / (N · V_T)) · exp(V_D_op / (N · V_T)).
C_j	Junction capacitance	Default 0. Stamped as admittance s · C_j in parallel with g_d.

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5. JFET (Shichman-Hodges depletion-mode)

NJFET / PJFET — depletion-mode field-effect transistors. The model is the same quadratic (V_GS_eff + VTO)² form as the L1 MOSFET in saturation, but with the threshold expressed as VTO (positive magnitude of the pinch-off voltage) and the device conducting at V_GS_eff = 0.

Code	Expanded name	Definition / units
BETA	Transconductance parameter	A/V². Plays the role of (1/2)·μ·Cox·(W/L) in the L1 MOSFET expression.
VTO	Pinch-off / threshold magnitude	Stored positive for both polarities (NJFET/PJFET).
LAMBDA	Channel-length modulation coefficient	1/V. λ = 0 reproduces ideal long-channel.
C_gs	Gate-source capacitance	Stamped as admittance s · C_gs in AC.
C_gd	Gate-drain capacitance	Stamped as admittance s · C_gd in AC.
V_GS_op, V_DS_op	Operating-point bias	Default to per-instance symbols if not supplied.
KF, AF, EF	Flicker noise parameters	Same form as the MOSFET flicker noise (§ 2.8).

Saturation drain current (for V_DS_eff ≥ V_ov, V_GS_eff ≥ −VTO):

I_D_mag = BETA · (V_GS_eff + VTO)² · (1 + LAMBDA · V_DS_eff)

Small-signal at the operating point: g_m = ∂I_D/∂V_GS, g_ds = ∂I_D/∂V_DS. Thermal channel noise reuses the L1 MOSFET form (4 · k_B · T · γ · g_m).

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6. Vacuum-tube triode (Langmuir 3/2 power)

Code	Expanded name	Definition
K	Perveance	A / V^(3/2). Geometry-dependent constant.
μ	Amplification factor mu	Dimensionless; obeys μ = g_m · r_p = g_m / g_p.
V_gk	Grid-cathode voltage	V(grid) − V(cathode)
V_pk	Plate-cathode voltage	V(plate) − V(cathode)
I_p	Plate current	I_p = K · (μ · V_gk + V_pk)^(3/2) (forward conduction only)
g_p	Plate conductance	∂I_p / ∂V_pk. Inverse r_p = 1 / g_p is plate resistance.
g_m	Triode transconductance	∂I_p / ∂V_gk = (3/2) · K · μ · √(μ V_g_op + V_p_op)
C_gk, C_gp, C_pk	Intrinsic interelectrode capacitances	Grid-cathode, grid-plate (Miller), plate-cathode.

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7. Voltage-controlled passive devices

7.1 Varactor (junction-capacitance model)

Voltage-controlled capacitor following the standard SPICE junction- capacitance form:

C(V) = C0 / (1 − V/V_J)^M

Code	Expanded name	Definition
C0	Zero-bias junction capacitance	F.
V_J	Junction (built-in) potential	V. Default 0.7.
M	Grading coefficient	Dimensionless. Default 0.5 (abrupt junction); 0.33 for linearly graded.
V_op	Operating-point bias across the varactor	Defaults to per-instance symbol V_op_<name> if not supplied.

The varactor is stamped in AC as the admittance s · C(V_op). It is inert at DC.

7.2 VSwitch (voltage-controlled smooth switch)

Smooth (tanh-shaped) resistance whose value depends on a control-port voltage V_c:

R(V_c) = R_off + (R_on − R_off) · ½ · (1 + tanh((V_c − V_t) / V_h))

Code	Expanded name	Definition
R_on	On-state resistance	Ω. Default 1.
R_off	Off-state resistance	Ω. Default 1 GΩ.
V_t	Threshold control voltage	V. The midpoint of the tanh transition.
V_h	Hysteresis-like transition width	V. Smaller V_h → sharper switch. Default 0.1.
V_c_op	Operating-point control voltage	Used to linearise the switch in AC.

The switch contributes a single conductance 1/R(V_c) between the two power-port nodes; the control port is a high-impedance pin and only samples V_c.

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8. Mutual inductance (MutualCoupling)

Couples two or more inductors via a shared coupling coefficient.

Code	Expanded name	Definition
k	Coupling coefficient	0 ≤ k ≤ 1; k = 1 is perfect coupling. Default 1.
M	Mutual inductance (derived per pair)	M_ij = k · √(L_i · L_j), computed from each pair of named inductors at stamping time.

In SPICE the same primitive is the K element. The MutualCoupling component takes a list of inductor names; SYCAN stamps the off-diagonal inductance entries in MNA so the mutual flux shows up as the expected voltage M_ij · ∂I_j/∂t (i.e. s · M_ij · I_j in AC).

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9. Transmission line

Code	Expanded name	Definition
Z0	Characteristic impedance	Ω. Real for the lossless model.
td	One-way time delay	s. td = ℓ / v for line length ℓ and phase velocity v.
loss	Total attenuation (lossy)	Nepers. Default 0 (lossless). The propagation θ = loss + s · td.
θ	Electrical length theta	θ = s · td for the lossless line; θ = loss + s · td when lossy.
γ	Propagation constant	γ · ℓ = (α + s/v) · ℓ, with the lossless case setting α = 0.

ABCD form (with θ = loss + s·td covering both lossless and lossy cases):

[V1]   [ cosh(θ)         Z0 · sinh(θ) ] [ V2 ]
[I1] = [ sinh(θ)/Z0      cosh(θ)      ] [-I2 ]

Y-matrix entries use coth(θ)/Z0 (self) and −csch(θ)/Z0 (mutual).

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10. Controlled sources (basic two-port primitives)

Code	Expanded name	SPICE form	Stamping behaviour
VCVS	Voltage-Controlled Voltage Source	Exxx N+ N- NC+ NC- gain	V(n+) − V(n−) = gain · (V(nc+) − V(nc−)). gain is dimensionless.
VCCS	Voltage-Controlled Current Source	Gxxx N+ N- NC+ NC- gain	Drives gain · (V(nc+) − V(nc−)) from n+ to n−. gain is a transconductance [S].
CCVS	Current-Controlled Voltage Source	Hxxx N+ N- VCTRL gain	V(n+) − V(n−) = gain · I(ctrl). gain is a trans-resistance [Ω].
CCCS	Current-Controlled Current Source	Fxxx N+ N- VCTRL gain	Drives gain · I(ctrl) from n+ to n−. gain is dimensionless.

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11. Behavioral sources (B-element)

Arbitrary-expression sources. The expression expr may reference any node-voltage symbol (V(node)); the components linearise it automatically for AC and noise analyses.

Component	Constraint enforced	Notes
BehavioralCurrent	Injects expr from n_plus to n_minus	Acts like a non-linear current source. V_op_subs (optional) supplies operating-point substitutions used during AC linearisation.
BehavioralVoltage	Forces V(n_plus) − V(n_minus) = expr	Acts like a non-linear voltage source; carries an auxiliary branch-current unknown. V_op_subs plays the same role as above.

Both are noise-less by construction (SUPPORTED_NOISE = frozenset()).

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12. Signal-flow blocks (sycan.components.blocks)

Higher-level abstract blocks, useful for behavioural top-down design (PLLs, ΣΔ modulators, etc.). Each is a single ideal voltage-mode I/O block with differential ports (in_p, in_m) → (out_p, out_m) unless stated otherwise.

Block	Constraint	Parameters
Gain	V(out_p) − V(out_m) = k · (V(in_p) − V(in_m))	k (voltage gain).
Integrator	H(s) = k / (s + leak)	k (DC gain numerator), leak (damping; 0 → ideal integrator), var.
Summer	V(out_p) − V(out_m) = Σ wᵢ · (V(in_p,i) − V(in_m,i))	inputs — list of (in_p, in_m, weight) tuples.
Quantizer	V(out_p) − V(out_m) = k_q · (V(in_p) − V(in_m)) + V_q	k_q (linear quantizer gain), plus an additive symbolic noise input.
TransferFunction	V(out_p) − V(out_m) = H(s) · (V(in_p) − V(in_m))	H (Laplace expression), var (default s).
OPAMP	Ideal single-VCVS op-amp: V(out) = A · (V(in_p) − V(in_m))	A (open-loop gain).
OPAMP1	First-order dominant-pole op-amp: H(s) = A · ω_p / (s + ω_p), with ω_p = 2π·GBW / A	A (DC open-loop gain), GBW (gain-bandwidth product, Hz), Z_out.

OPAMP and OPAMP1 are implemented as SubCircuits — see § 13.

12.1 OPAMP1 derived quantities

Code	Expanded name	Definition
A	DC open-loop gain	H(0) of the OPAMP1 transfer function.
GBW	Gain-bandwidth product	Hz. Unity-gain frequency.
ω_p	Dominant pole	ω_p = 2π · GBW / A.
Z_out	Output impedance	Optional series output Z. None ⇒ ideal voltage output.

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13. SubCircuit (sycan.components.blocks.subcircuit)

Hierarchical instantiation of a body Circuit into a parent. The port_map dict maps each pin name in the inner body to its external parent-circuit node. At stamping time the SubCircuit flattens its body into the parent MNA system with name-mangled internal nodes, so a sub-circuit instance contributes the same equations its body would have contributed if pasted in line.

Code	Expanded name	Notes
body	Inner Circuit	Defines the reusable block.
port_map	{body_pin: parent_node} mapping	Names every external connection point of the block.

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14. Voltage source waveforms (VoltageSource)

In addition to a DC value and an AC-phasor ac_value, a voltage source may declare a time-domain waveform, whose Laplace transform is stamped on the right-hand side of the MNA system in ac mode.

Waveform	Parameters	Laplace transform
"sine"	amplitude, frequency, phase	A · (s · sin(φ) + ω · cos(φ)) / (s² + ω²) with ω = 2π·frequency.
"pulse"	v1, v2, td, pw	Single rectangular pulse: v1/s + (v2−v1)·(exp(−s·td) − exp(−s·(td+pw)))/s.
"exp"	v1, v2, td1, tau1, td2?, tau2?	Exponential pulse rising toward v2 with tau1, optionally recovering to v1 with tau2.

DC values are picked up automatically from the waveform parameters (e.g. value = v1 for pulse/exp).

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15. MNA & analysis terms

Code / Term	Expanded
MNA	Modified Nodal Analysis. Linear system A · x = b whose unknowns are node voltages plus a few branch currents.
KCL	Kirchhoff’s Current Law. The MNA row equations are KCL at each non-ground node.
KVL	Kirchhoff’s Voltage Law.
A	MNA matrix (admittances + auxiliary stamps).
x	Unknown vector — node voltages followed by auxiliary branch currents (one per V/E/H source, etc.).
b	Right-hand side — independent excitations.
s	Laplace variable. Capacitor stamps s · C; inductor stamps 1 / (s · L).
aux	Auxiliary branch current — extra unknown row used by elements that can’t be stamped as plain admittances (V-source, VCVS/CCVS/CCCS, DC inductor, DC TLINE).
has_nonlinear	Class flag: component contributes transcendental KCL terms via stamp_nonlinear (diode, BJT, MOSFET, JFET, triode, behavioral, varactor, vswitch).
G_MIN	SPICE GMIN shunt — a 1 GΩ conductance from every node to ground used during damped Newton to keep the Jacobian conditioned at flat operating points.
freq	Real-valued frequency symbol exposed by sycan.mna. Used by flicker-noise PSDs (which carry 1/freq^EF) since s = jω is not a useful argument for a real PSD.

15.1 Analysis modes

Mode	Component behaviour
dc	Capacitors → open, inductors → 0 V source (short via auxiliary current). Nonlinear models contribute residuals.
ac	Small-signal Laplace-domain stamps. Capacitors → s · C, inductors → 1 / (s · L). Nonlinear devices → linearised at their operating point (g_m, g_ds, intrinsic caps).

15.2 Solvers (sycan.mna)

Solver	Purpose
solve_dc	DC operating point. Linear systems → symbolic LU; nonlinear → CAS solver on full residual system.
solve_dc_sweep	Sweep one symbolic parameter across values and substitute into the symbolic DC solution. Closed-form .DC.
solve_ac	Small-signal Laplace-domain solve. Returns {Symbol(V(node)): expr(s)}.
solve_tf	Transfer function H(s) = V(output_node) / source_value. Returns dict with H, dc_gain, hf_gain, numerator, denominator.
solve_pz	Pole-zero analysis: factors H(s) to extract poles (denominator roots) and zeros (numerator roots). Returns PZResult.
solve_impedance	Port impedance (input/output) at a labelled port, with termination="auto" choosing excitation/loading.
solve_noise	Output-referred noise PSD. Returns (S_total, per_source) — S_total and a dict of per-noise-source contributions.
solve_sensitivity	∂V_out/∂p for each parameter, in DC or AC mode. normalized=True reports (p / V_out) · ∂V_out/∂p.

PZResult is a small record carrying H, numerator, denominator, poles, and zeros.

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16. ERC / DRC (sycan.check)

Read-only structural checks on a Circuit. check_circuit(circuit) returns an ERCReport.

Code	Severity	Meaning
DUPLICATE_NAME	error	Two components share a designator after sub-circuit flattening.
PIN_SHORT	warning	Two pins of the same component land on the same node (self-loop / pin tie).
DANGLING_NODE	warning	A node is referenced by exactly one pin — almost always a typo.
NO_GROUND	error	No ground node ("0" / GND) exists in the flattened netlist.
FLOATING_GROUND	error	A pin connects to ground but ground itself isn’t tied to anything else.
ISLAND	warning	Two or more disjoint connected components — the netlist isn’t one circuit.

ERCReport exposes:

Attribute	Meaning
findings	List of ERCFinding(severity, code, message).
errors	Findings with severity == "error".
warnings	Findings with severity == "warning".
ok	True iff there are no error-severity findings.

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17. Network parameters (sycan.network_params)

Two-port (and n-port where it applies) representations:

Code	Name	Defining relation
Z	Impedance parameters	V = Z · I
Y	Admittance parameters	I = Y · V
S	Scattering parameters	b = S · a, with reference impedance Z0
ABCD	Chain (transmission) matrix	[V1; I1] = ABCD · [V2; −I2] (2-port only)
T	Transfer / scattering-transfer	[a1; b1] = T · [b2; a2] (2-port only)

a and b are the incident and reflected normalised power waves; Z0 is the per-port reference impedance (default 50 Ω).

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18. Noise

Code	Expanded
PSD	Power Spectral Density [V²/Hz or A²/Hz].
S_V_out	Output-voltage noise PSD.
H_k(s)	Trans-impedance from the k-th unit-current noise source to the output node.
S_k	One-sided current-noise PSD of the k-th source.
γ (noise)	Long-channel channel-thermal-noise excess factor; _NOISE_GAMMA = 2/3 in the L1/4T MOSFETs.
thermal	Johnson-Nyquist thermal noise. Resistor PSD: 4 · k_B · T / R. MOSFET / JFET channel PSD: 4 · k_B · T · γ · g_m.
shot	Schottky shot noise, 2 · q · I_op (one-sided). Used by Diode, BJT (×2), sub-threshold MOSFET.
flicker	1/f noise: KF · I_op^AF / freq^EF. Emitted by the L1/3T/4T/subthreshold MOSFETs, JFET, and BJT.

The noise superposition formula used by solve_noise:

S_V_out(s) = Σ_k  H_k(s) · H_k(−s) · S_k

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19. Filter prototypes (sycan.polynomials)

All return (numerator, denominator) in the Laplace variable s, normalised to |H(0)| = 1 and 1 rad/s cutoff.

Function	Family
butterworth	Butterworth — maximally flat magnitude in the passband.
chebyshev1	Chebyshev Type I — equiripple in the passband, monotonic in the stopband.
bessel	Bessel — maximally flat group delay (linear phase).

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20. Headroom analysis (sycan.headroom)

Term	Meaning
Headroom	Range of an input variable (a single source value or a coupled group) over which every MOSFET stays in saturation.
HeadroomResult	Returned record with intervals, boundaries, samples, widest, and binding_devices().
Binding device	The transistor that exits saturation at a given interval edge — the one setting the headroom on that side.
V_id	Differential input voltage in a differential-pair sweep (typical use case in the headroom docstring).

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21. Acronym quick-reference

Acronym	Expanded
MOSFET	Metal-Oxide-Semiconductor Field-Effect Transistor.
NMOS	n-channel MOSFET.
PMOS	p-channel MOSFET.
JFET	Junction Field-Effect Transistor.
NJFET / PJFET	n-channel / p-channel JFET.
BJT	Bipolar Junction Transistor.
NPN/PNP	BJT polarities; npn = n-emitter/p-base/n-collector, pnp the opposite.
L1	Shichman-Hodges Level 1 — the original SPICE long-channel quadratic MOSFET model.
3T / 4T	Three-terminal (bulk tied to source) / four-terminal (bulk exposed) MOSFET wrapper.
MNA	Modified Nodal Analysis.
ERC	Electrical Rule Check (sycan.check.check_circuit).
DRC	Design Rule Check — used interchangeably with ERC in this codebase.
SPICE	Simulation Program with Integrated Circuit Emphasis. Reference for sign conventions and parameter names.
DC	Direct-current operating point.
AC	Small-signal alternating-current (Laplace) analysis.
TF	Transfer Function (solve_tf).
PZ	Pole-Zero analysis (solve_pz).
GBW	Gain-bandwidth product (OPAMP1).
RF	Radio-frequency (the components.rf package — currently the lossless transmission line).
TLINE	Transmission line.
VCO/Vctrl	Naming convention for the controlling source of a CCCS/CCVS.
VCVS / VCCS / CCVS / CCCS	Voltage- / Current-Controlled Voltage / Current Source primitives.
ABCD	Chain / transmission matrix.
PSD	Power Spectral Density.
GMIN	SPICE shunt conductance from every node to ground used to keep the Jacobian conditioned.
KF / AF / EF	Flicker (1/f) noise coefficient / current exponent / frequency exponent.
B-element	Behavioral source (BehavioralVoltage, BehavioralCurrent).