What You Need Before Starting
- Source impedance Z_s (usually 50 Ω system impedance)
- Load impedance Z_L = R_L + jX_L at the design frequency f₀ (from S-parameter measurement or datasheet)
- Target return loss (e.g., S11 < −10 dB across ±10% bandwidth)
An L-network uses exactly two reactive elements — one in series and one in shunt — to transform one impedance to another. The topology is determined by whether R_L < Z₀ (step-up, shunt-first) or R_L > Z₀ (step-down, series-first).
Step 1: Identify the Impedance Ratio and Q
Given: Z_s = 50 Ω, R_L = 10 Ω (PA output, typical GaN device) Ratio: Z_s / R_L = 5 → R_L < Z₀ → use shunt-first (parallel C, series L) Q = √(Z_s/R_L − 1) = √(50/10 − 1) = √4 = 2.0 BW ≈ f₀ / Q = 900 MHz / 2 = 450 MHz (3 dB bandwidth of the match)
Step 2: Calculate Reactance Values
Shunt element (at input, 50 Ω side):
X_shunt = Z_s / Q = 50 / 2 = 25 Ω (capacitive: X_C = −25 Ω)
→ C_shunt = 1/(2π · f₀ · |X_C|) = 1/(2π · 900e6 · 25) = 7.07 pF
Series element (at output, R_L side):
X_series = Q · R_L = 2 · 10 = 20 Ω (inductive: X_L = +20 Ω)
→ L_series = X_L / (2π · f₀) = 20 / (2π · 900e6) = 3.54 nH
Circuit: 50Ω ── [shunt 7.07 pF] ── [series 3.54 nH] ── 10Ω
Step 3: Cancel Load Reactance
If the load has a reactive component (X_L ≠ 0), add a series element to cancel it:
Z_L = 10 − j8 Ω (capacitive at f₀) Add series inductor to cancel: X_cancel = +j8 Ω → L_cancel = 8 / (2π · 900e6) = 1.41 nH in series with load Total series inductance = 3.54 + 1.41 = 4.95 nH (can combine into one inductor)
Step 4: Verify on Smith Chart
- Start at load point (10 − j8 Ω) / 50 = 0.2 − j0.16 (normalized)
- Add series inductor: move clockwise on constant-r=0.2 circle
- Add shunt capacitor: move on admittance chart counter-clockwise
- Target: center of chart (1 + j0) = 50 Ω matched
Step 5: Choose Real Component Values
C = 7.07 pF → pick 6.8 pF (C0G, ±0.5 pF, Q > 500 at 900 MHz) L = 4.95 nH → pick 4.7 nH (±5%, Q ≥ 50 at 900 MHz) Adjust with simulation: retune shunt C slightly to compensate for inductor self-resonance and layout parasitics
Step 6: Simulate and Measure
- Load the S2P of the device into RF View Circuit Simulator as an S2P block
- Add the shunt C and series L elements
- Simulate S11 — target < −10 dB (ideally < −14 dB) across operating band
- Run Monte Carlo with ±5% component tolerance to verify yield
RF View Auto Matching: Skip the manual calculation. Load your device .s2p or .s1p file, set target frequency 900 MHz, and tap "Auto Match." RF View computes the optimum L-network values instantly. Switch to "Real Match" to auto-substitute Murata catalog components. Available free on Android.
Design Tips:
- High impedance ratio → high Q → narrow bandwidth. Use a two-section (Pi/T) design for broader bandwidth.
- Always use C0G/NP0 capacitors, not X7R, for RF matching networks — X7R has poor Q and shifts with temperature.
- Minimize trace length between matching components to reduce layout parasitics.