S-Parameters & RF Performance

RF checks for matching, transmission, isolation, coupling, phase response, and

standing-wave behavior.

#	VER ID	Parameter	Severity	Design Rule / Constraint	Ideal / Optimal Value	Acceptable Range	Good	Bad	Why It Matters
1	HFSS-S-001	Return Loss	Critical	S11 ≤ −20 dB at operating frequency	< −20 dB	−15 to −25 dB	< −20 dB: excellent impedance match; full power into resonator/qubit	> −10 dB: >10% power reflected; readout chain SNR degraded	Reflected power from input port. Poor return loss = impedance mismatch → signal reflections degrade qubit readout fidelity.
2	HFSS-S-002	Insertion Loss	Critical	S21 ≥ −0.1 dB in passband	< −0.1 dB	−0.1 to −1 dB	< −0.1 dB: near-lossless transmission; signal integrity preserved	> −3 dB: half power lost; readout SNR < 3 dB, fidelity severely impacted	Signal transmission efficiency. High insertion loss reduces readout SNR, requiring higher drive power that heats the device.
3	HFSS-S-003	Transmission |S21|	High	|S21| ≥ 0.95 (linear) in passband	≈ 1.0 (unity)	0.9 – 1.0	≥ 0.95: >90% amplitude transmission; strong coupling confirmed	< 0.5: >50% amplitude loss; readout inefficient	Linear magnitude of S21. Near-unity confirms full coupling efficiency; used in EPR extraction and resonator characterisation.
4	HFSS-S-004	Port Isolation	High	Sij ≤ −30 dB between non-coupled ports	< −30 dB	−20 to −40 dB	< −30 dB: crosstalk negligible; simultaneous multi-qubit readout viable	> −15 dB: strong port coupling; driven rotations on idle qubits	Cross-port electromagnetic isolation. Insufficient isolation causes simultaneous readout errors and qubit–qubit cross-drive.
5	HFSS-S-005	Forward Isolation (S12)	High	S12 ≤ −20 dB (Purcell filter context)	< −20 dB	−15 to −30 dB	< −20 dB: amplifier backaction blocked; qubit protected from output noise	> −10 dB: HEMT noise reaches qubit; excess excitation and T₁ degradation	Reverse isolation prevents HEMT amplifier noise photons from reaching qubit. Critical in Purcell filter and circulator design.
6	HFSS-S-006	Phase of S21 (GDD)	Medium	Group delay deviation < 1 ns across qubit bandwidth	Linear phase	< 5° deviation	Linear phase: negligible pulse distortion; gate calibration stable	Non-linear phase: pulse distortion → systematic gate errors	Non-linear phase response causes group delay dispersion that distorts shaped control pulses, increasing gate error.
7	HFSS-S-007	Coupling Coefficient κ	Critical	1 MHz ≤ κ/2π ≤ 10 MHz (readout resonator)	1 – 5 MHz	0.5 – 20 MHz	1–5 MHz: fast readout (< 1 µs) with Purcell rate < 1 kHz; near quantum limit	< 0.1 MHz: readout > 10 µs; > 100 MHz: Purcell collapse of T₁	External coupling rate of readout resonator. Sets fundamental trade-off between measurement speed and Purcell-induced qubit decay.
8	HFSS-S-008	VSWR	Medium	VSWR ≤ 1.1 : 1 at operating frequency	< 1.1 : 1	1.1 – 1.5 : 1	< 1.1:1: >99% power transfer; standing waves negligible	> 2.0:1: standing waves cause frequency-dependent errors	Voltage standing wave ratio quantifies impedance mismatch. High VSWR degrades power delivery to qubit and readout resonator.