T Matching Network Calculator

T-Network Impedance Matching Estimator

T Matching Network Formula

Formula

\[ X = Q \, R_s \\ B = \frac{Q}{R_s} \\ L_s = L_l = \frac{X}{2\pi f} \\ C = \frac{B}{2\pi f} \]

Where:

\(f\) — operating frequency (Hz)
\(R_s\) — source resistance (Ω)
\(Q\) — loaded quality factor of the network
\(X\) — required series reactance (Ω)
\(B\) — required shunt susceptance (S)
\(L_s, L_l\) — series inductances (H)
\(C\) — shunt capacitance (F)

Each series arm of the T network needs a reactance of \(X = QR_s\), and the shunt branch needs a susceptance of \(B = Q/R_s\). Dividing by \(2\pi f\) converts the reactance into an inductance and the susceptance into a capacitance at the operating frequency.

T Matching Network – Calculation Example

Example: match a 50 Ω source to a 100 Ω load at 1 MHz with a quality factor of 2 — the calculator's default values.

\[ X = Q R_s = 2 \times 50 = 100~\Omega \]

\[ B = \frac{Q}{R_s} = \frac{2}{50} = 0.04~\text{S} \]

\[ L_s = L_l = \frac{100}{2\pi \times 1\,000\,000} \approx 15.92~\mu\text{H} \]

\[ C = \frac{0.04}{2\pi \times 1\,000\,000} \approx 6.37~\text{nF} \]

Result: two series inductors of 15.92 µH and a shunt capacitor of 6.37 nF.

How to Use the Calculator

Enter the operating Frequency in hertz (for example, 1000000 for 1 MHz).
Enter the Source Resistance and Source Reactance in ohms — the real and imaginary parts of the impedance driving the network.
Enter the Load Resistance and Load Reactance in ohms — the impedance the network must match to.
Set the Q Factor. Higher Q gives stronger harmonic attenuation but narrower bandwidth; typical values are 1–5.
Choose Circuit DC Current: “Pass DC Current” keeps the series inductors so DC flows through the network, while “Block DC Current” indicates series capacitors that isolate the DC path.
Read the three component values from the results: the shunt capacitor \(C\) and the two inductors \(L_s\) and \(L_l\).

What Is a T Matching Network?

A T matching network is a three-element impedance transformation circuit named after its shape: two reactive elements in series (one in each arm of the signal path) and a third reactive element connected as a shunt between them. In the low-pass configuration computed here, the series arms are inductors and the shunt element is a capacitor. It is widely used in radio-frequency design — between a transmitter and an antenna, an amplifier and a filter, or a source and a transmission line — to transform one impedance into another.

Matching matters because of the maximum power transfer theorem: when the impedance seen by the source equals the complex conjugate of the source impedance, the largest possible fraction of power is delivered and reflections vanish. Without a match, part of the signal reflects back toward the source, producing standing waves (a high VSWR), reduced transmitted power, inaccurate measurements, and — in transmitters — stress on the output stage.

The quality factor \(Q\) sets how aggressive the transformation is. A higher Q means larger reactances, a steeper impedance transformation, and stronger attenuation of harmonics; the low-pass T with series inductors and a shunt capacitor passes the fundamental while attenuating higher frequencies. The trade-off is bandwidth: higher Q narrows the frequency range over which the match holds and makes the circuit more sensitive to component tolerances and frequency drift.

Compared with the two-element L network, whose Q is fixed by the impedance ratio, the T network lets you choose the Q — and therefore the bandwidth — independently. Its close relative, the PI network impedance matching calculator, uses two shunt elements and one series element and is often preferred when a shunt capacitor at the load is more convenient.

Assumptions, Limitations and Practical Tips

The calculation assumes ideal, lossless components. Real inductors have winding resistance and self-capacitance, which shift the match at higher frequencies; use RF-grade components and verify with a network analyzer if accuracy is critical.
The component values are derived from the resistive part of the source impedance. If your source or load has significant reactance, cancel it first — for example, a capacitive load reactance can be absorbed by reducing the adjacent series inductive reactance by the same amount.
Both series arms use the same reactance \(X = QR_s\), which produces an exact conjugate match when \(R_l = R_s(1+Q^2)\). For other load resistances the result is an approximation; check the final impedance with a Smith chart or circuit simulator and adjust Q or the load-side component if needed.
The “Block DC Current” option changes the component types rather than the required reactances: series capacitors of \(1/(2\pi f X)\) farads replace the series inductors, so DC is isolated while the RF match is preserved.
All component values scale inversely with frequency — the same reactances at 10 MHz need one-tenth the inductance and capacitance as at 1 MHz.
When building the network, keep leads short and account for parasitic inductance; the straight wire inductance calculator helps estimate how much a lead or trace adds. If an exact value is unavailable, combine stock parts using the series inductance and parallel inductance calculators.

Frequently Asked Questions

How do I calculate a T matching network by hand without the calculator?

First pick your Q, then compute the series reactance as X = Q × Rs and the shunt susceptance as B = Q ÷ Rs. Convert them to real components at your frequency: \(L = X / (2\pi f)\) for each series inductor and \(C = B / (2\pi f)\) for the shunt capacitor. For example, with a 50 Ω source at 7 MHz and Q = 3, X = 150 Ω gives about 3.4 µH per coil, and B = 0.06 S gives roughly 1.4 nF.

What is a good Q factor to use for a T matching network?

Most practical designs use Q between 1 and 5. A Q of 1–2 gives a wideband, tolerant match suited to antenna tuners and general RF work. Q of 3–5 narrows the bandwidth but attenuates harmonics more strongly, which helps in transmitter output stages. Remember that Q is tied to the achievable impedance ratio: an exact match requires \(R_l = R_s(1+Q^2)\), so you cannot pick Q freely for a given resistance pair.

How do I convert between henries, farads and their sub-units?

RF values are usually small, so you will see micro (µ), nano (n) and pico (p) prefixes. 1 H = 10⁶ µH = 10⁹ nH, and 1 F = 10⁶ µF = 10⁹ nF = 10¹² pF. So a calculator result of 0.00001592 H is 15.92 µH, and 0.00000000637 F is 6.37 nF. If the frequency is given in MHz, use \(f = 10^6 \times \text{MHz}\) before dividing.

Can I use this calculator with a complex or reactive load, like a real antenna?

Only approximately. The formulas assume purely resistive terminations. If your load has reactance, first cancel it — subtract a capacitive load reactance from the adjacent series inductive reactance, or add the opposite reactance externally — and feed the remaining resistance into the calculator. Real antennas often present an impedance like \(35 - j12\) Ω; treat the 12 Ω separately, then verify the finished network on a VNA or with a VSWR meter.

Why doesn't my built circuit match perfectly? Common mistakes.

Frequent culprits: component tolerance and parasitics (inductor self-capacitance and winding resistance shift the response at VHF and above), long leads adding unwanted inductance, and load resistance far from \(R_s(1+Q^2)\), where the simple formulas become an approximation. Also check that you entered frequency in hertz, not megahertz — a factor-of-a-million error is the most common input mistake. Simulate the final values in a circuit simulator before soldering.

T network vs. PI network vs. L network — which should I choose?

An L network uses only two components but its Q is fixed by the impedance ratio, so you cannot control bandwidth. A T network (series–shunt–series) lets you choose Q and passes DC through its series inductors — handy when bias current must reach the load. A PI network (shunt–series–shunt) also allows free Q choice and naturally blocks DC; it is common in tube-transmitter output stages. Pick based on DC path needs and where a shunt capacitor is physically convenient.

How do I size the series capacitors if I select 'Block DC Current'?

The required reactance stays the same — only the component type changes. Each series inductor is replaced by a capacitor with the same reactance X at your operating frequency: \(C = 1 / (2\pi f X)\) farads. For example, if X = 100 Ω at 1 MHz, you need two series capacitors of about 1.59 nF each. The shunt element is unaffected. Make sure the capacitors' voltage rating covers both the RF swing and any DC present.