Impedance Matching Synthesis

matchedRF

Automated broadband impedance matching network synthesis for RF power amplifiers. Fano-Optimum Chebyshev solutions with user-directed Norton transform explorer. No optimization algorithms — direct procedural synthesis.

Download on App Store Design Flow

Example: Interstage Matching Network — Order 4, Fano Optimized

How It Works

Typical Design Flow

Input Parameters

Enter your amplifier requirements and transistor properties.

RF bandwidth (Start / Stop GHz)
Termination 1: Series or Parallel RC (Rin/Ropt + C_parasitic)
Termination 2: Series or Parallel RC (Ropt + C_parasitic)
Network order (2, 4, or 6)
Enable Fano Optimum toggle

Auto-Solve & Transform

matchedRF synthesizes the matching network and presents available solutions.

Chebyshev Bandpass solution generated instantly
Norton Transform Explorer shows N1, N2, N3 sliders
Guided or user-directed transformer selection
Transformation linkage ensures proper terminations
Q-Adjusted solutions for low-Q situations

Export

Export the final design in multiple formats for implementation and documentation.

Schematic + design summary PDF
LC component listing (.csv)
S-parameters (.s2p)
matchedRF native format (.pamatch)
Compatible with any 3rd-party CAD tool

Capabilities

Key Features

⋆

Fano-Optimum Solution

Maximum theoretical matching performance using Fano's design criterion. Best possible insertion and return loss within the specified bandwidth.

⊃

Capacitive Absorption

Absorb transistor parasitics (Cgs, Cds) into the matching network for maximum bandwidth. Makes interstage matching straightforward.

≈

Chebyshev Bandpass Order 2–6

Lumped-element Chebyshev bandpass topologies. Higher network order provides steeper rolloff and better out-of-band rejection.

⟳

Norton Transform Explorer

User-directed or guided Norton transformer selection. Adjust component values without changing the frequency response. Linked transformers ensure proper terminations.

Q-Adjusted Solutions

Special solution class for low-Q matching situations. Inflates Q minimally to enable transforms, reducing required network order with modest performance trade-off.

📊

Frequency Response Plots

Real-time visualization of insertion loss, return loss, transmission phase, and group delay. Switch domain with a long-tap on the frequency axis.

⊞

Schematic View

Toggle between full schematic view and component grid view. All Norton transforms clearly labeled and bracketed for easy identification.

↗

Direct Synthesis

Procedural, closed-form synthesis — no iterative optimization. Deterministic results in milliseconds based on Matthaei, Dawson, and Levy's analytical methods.

⊞

Multiple Matching Scenarios

Directly applicable to input matching, output matching, and interstage matching in RFIC and millimeter-wave power amplifier design.

Design Example

Interstage Matching — 5G NR Bands N77+N78+N79

Design a 2-stage interstage match for a FET power amplifier covering 3.3–5.0 GHz. The output of Stage 1 (200Ω + 0.125 pF parallel RC) must be matched to the input of Stage 2 (1.25Ω + 10.0 pF series RC).

Device Parameters

Two-stage FET PA transistor properties

	Cgs (pF)	Rgs (Ω)	Ropt (Ω)	Cds (pF)
PA Stage 1	1.0	12.5	200	0.125
PA Stage 2	10.0	1.25	20	1.250

matchedRF Inputs

Term 1 200Ω ∥ 0.125 pF

Term 2 1.25Ω + 10.0 pF

BW 3.2 – 5.1 GHz

Order n = 4, Fano Optimum

Result

Q1: 0.6346  ·  Q2: 3.152

2 Possible Solutions

IL: −0.14 dB  ·  Ripple: 0.05 dB

N1=4.121 · N2=0.434 · N3=5.889

Schematic

Chebyshev n=4, Fano Optimized · 3 Norton Transforms

Component Listing

14 components, 3 Norton transforms, cumulative ratio 111.1×

Components

              R1 = 200 Ω

              C1 = 0.125 pF

              C3 = 0.171 pF

              L_N1_1 = 3965 pH

              L_N1_2 = 1279 pH

              L_N1_3 = 327.5 pH

              C_N2_1 = 1.401 pF

              C_N2_2 = 4.688 pF

              C_N2_3 = 3.618 pF

              L_N3_1 = 2446 pH

              L_N3_2 = 915.8 pH

              L_N3_3 = 186.9 pH

              C2 = 10 pF

              R2 = 1.25 Ω

Frequency Response

Academic Foundations

References

[1]

G. Matthaei, L. Young, and E. M. T. Jones, Microwave Filters, Impedance Matching Networks, and Coupling Structures. New York: McGraw-Hill, 1964; Norwood, MA: Artech House, 1980.

[2]

D. E. Dawson, "Closed-form solutions for the design of optimum matching networks," IEEE Trans. Microw. Theory Tech., vol. 57, no. 1, pp. 121–129, Jan. 2009.

[3]

R. Levy, "Explicit formulas for Chebyshev impedance-matching networks, filters, and interstages," Proc. Inst. Elect. Eng., vol. 111, no. 6, pp. 1099–1106, Jun. 1964.

[4]

T. E. Shea, Transmission Networks and Wave Filters. New York: Van Nostrand, 1929, p. 325.