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Back to Learning StudioEXECUTABLE RF METHODS · D0
From equation to circuit
Edit a real analytical network, inspect its response, and keep a reproducible design revision.
References and the calculations here work in this browser. For physical lessons, use Read runtime context or Read whole-filter runtime context below. Local development uses the configured server proxy; hosted physical workflows require a paired runtime. These controls check availability before generation. An unavailable direct tool connection does not disable the local lesson proxy.
LC ladder synthesis
Revision 1 · method 6.0.0Generated circuit
Click an element to inspect · shared return node 0Loaded circuit response
| Object | Placement / connection | Current value | Controlled edit |
|---|---|---|---|
| S1: series / single | |||
| S2: shunt / single | |||
| S3: series / single | |||
| S4: shunt / single | |||
| S5: series / single |
SPICE export contains this circuit and fixed ESR where requested; no SPICE solver is executed here. A physical seed is unbound until a runtime resolves real primitives and their evidence.
Calculated outputs and check scope
{
"reference_response": {
"s21": {
"re": -0.49999999999999967,
"im": 0.5000000000000002
},
"s11": {
"re": -0.5000000000000003,
"im": -0.4999999999999999
},
"transmissionDb": -3.0102999566398125,
"reflectionDb": -3.01029995663981,
"phaseRad": 2.3561944901923444,
"acceptedFraction": 0.4999999999999998,
"transmittedFraction": 0.4999999999999999,
"lossFraction": -1.1102230246251565e-16
}
}Intermediate values · normalized SI inputs
{
"inputs": {
"family": "butterworth",
"type": "lp",
"order": 5,
"rOhm": 50,
"f1Hz": 1000000000,
"f2Hz": 2000000000,
"rippleDb": 0.5,
"q": null
},
"intermediates": {
"reference_frequency_hz": 1000000000,
"angular_reference_frequency_rad_s": 6283185307.179586,
"source_resistance_ohm": 50,
"load_resistance_ohm": 50,
"load_ratio": 1,
"prototype": {
"g": [
0.6180339887498948,
1.618033988749895,
2,
1.618033988749895,
0.618033988749895
],
"loadRatio": 1
},
"prototype_order": 5,
"realized_reactive_order": 5,
"angular_bandwidth_rad_s": 0
}
}Bind a capacitor to the local process
Generate the selected circuit target with the runtime’s admitted CMIM primitive. This creates a separate inspectable component; it does not adopt it into the transmitter.
Read runtime context to check the current design and capability. Local development uses the configured lesson proxy independently of standalone-tool pairing; hosted pages require a paired runtime. Analytical lessons remain available offline.
Generate or inspect a whole filter
The existing runtime queue generates the full L–C–L circuit with finite signal and return access. This is separate source geometry, not a qualified physical filter response.
Read whole-filter runtime context to check the authoritative design and generation capability. Local development uses the configured lesson proxy independently of standalone-tool pairing; hosted pages require a paired runtime. File inspection remains available offline.
Whole-filter generation currently requires an explicit three-element series L / shunt C / series L lesson. Change synthesis inputs explicitly; the UI does not replace your circuit.
Method, derivation and limits
- Orders 1–9; Butterworth or Chebyshev I.
- Series-first ladder, real positive terminations. Even Chebyshev retains its unequal load.
- Ideal lumped elements or explicitly constant ESR; no process binding.
prototype.chebyshev
ε = √(10^(Rp/10) − 1); η = asinh(1/ε); γ = sinh(η/N); aₖ = sin[(2k−1)π/(2N)]; g₁ = 2a₁/γ; gₖ = 4aₖ₋₁aₖ / [(γ² + sin²((k−1)π/N))gₖ₋₁]. Even N: Rload/Rsource = coth²(η/2).
SciPy: Chebyshev-I analog prototypetransform.bp
B = ω₂ − ω₁; ω₀ = √(ω₁ω₂). Series LC: L = Rg/B, C = B/(Rgω₀²). Shunt parallel LC: L = RB/(gω₀²), C = g/(RB).
SciPy: low-pass to band-passtransform.bs
Series parallel LC: L = RgB/ω₀², C = 1/(RgB). Shunt series LC: L = R/(gB), C = gB/(Rω₀²).
SciPy: low-pass to band-stopnetwork.power-waves
Dₙ = A Rload + B + C Rsource Rload + D Rsource; S21 = 2√(Rsource Rload)/Dₙ. Series Z: [1 Z; 0 1]; shunt Y: [1 0; Y 1]. Matrices multiply in circuit order.
scikit-rf: network conventionsloss.fixed-esr
ZL = rL + jωL; ZC = rC − j/(ωC); rL = ωref L/Q; rC = 1/(ωref C Q). These resistances stay constant during the sweep.
ngspice manual: linear circuit elementsSources identify the analytical method. They do not qualify a process device or the 60 GHz transmitter. Saved sessions retain inputs, explicit edits and circuit identity; reopening recomputes instead of trusting imported metrics.