T-Pad Attenuator Calculator computes series and shunt resistor values for a symmetrical attenuator pad, along with exact voltage ratio, power ratio, and resistor heat dissipation.
T-Pad Attenuator Calculator: Resistor Values for Impedance-Matched RF Pads
This calculator computes the series and shunt resistor values for a symmetrical T-pad attenuator that reduces signal level by a set number of decibels while keeping the input and output impedance matched to $Z_0$. RF technicians, broadcast engineers, and amateur radio operators use it to build fixed attenuator pads for signal generators, receivers, and test equipment.
T-Pad Calculator Inputs and Outputs
Enter the characteristic impedance $Z_0$ in ohms and the desired attenuation $A_{dB}$ in dB. The calculator returns the two series resistors $R_1$ and the shunt resistor $R_2$ in ohms, the voltage and power ratios, the equivalent Pi-pad resistor set, and the heat dissipated by each resistor for a given input power.
How the T-Pad Formula Works
Per the ARRL Handbook for Radio Amateurs, T-pad design starts with the voltage ratio, or K-factor:
$$K = 10^{A_{dB}/20}$$
The two series arms and the shunt arm are then:
$$R_1 = Z_0\left(\dfrac{K-1}{K+1}\right) \qquad R_2 = Z_0\left(\dfrac{2K}{K^2-1}\right)$$
Attenuation in nepers is $\ln(K)$, power ratio is $K^2$, and the transmission coefficient is $S_{21} = 1/K$. The equivalent Pi-pad values, for the same $Z_0$ and $A_{dB}$, are $R_s = Z_0(K^2-1)/(2K)$ for the series arm and $R_p = Z_0(K+1)/(K-1)$ for each shunt arm. The most common input mistake is applying the power-ratio exponent instead of the voltage-ratio one — using $K = 10^{A_{dB}/10}$ instead of $10^{A_{dB}/20}$ — which produces a pad with roughly double the intended attenuation.
A detail that doesn’t show up on most T-pad tools: although both series resistors carry the identical calculated value of $R_1$, they do not dissipate equal power once a signal is actually applied.
Current entering the pad is highest before it reaches the shunt node, so the input-side $R_1$ dissipates several times more heat than the output-side $R_1$ — at 10 dB into a matched 50 Ω pad with 1 W in, the input resistor dissipates roughly ten times what the output resistor does, even though their resistance is the same. Power-rating both series resistors identically, as many builders do, over-specifies the output resistor and under-specifies the input one.
Symmetrical T-Pad Topology
T-Pad Resistor Values for Standard 50 Ω Attenuation Steps
The values below are calculated with the formula above at $Z_0 = 50\ \Omega$, the industry-standard RF impedance, for the attenuation steps most commonly stocked as fixed pads.
| Attenuation (dB) | K-Factor | R1 (Ω) | R2 (Ω) |
|---|---|---|---|
| 1 | 1.122 | 2.88 | 433.34 |
| 3 | 1.413 | 8.55 | 141.95 |
| 6 | 1.995 | 16.62 | 66.93 |
| 10 | 3.162 | 25.97 | 35.14 |
| 20 | 10.000 | 40.91 | 10.10 |
| 30 | 31.623 | 46.93 | 3.17 |
T-Pad Attenuator Design: Common Questions
What does the K-factor represent in a T-pad design?
K is the voltage ratio between input and output, $K = 10^{A_{dB}/20}$. It’s the single value both resistor formulas are built from, which is why RF handbooks tabulate K before R1 and R2.
Can a T-pad be built with unequal source and load impedances?
Not with the symmetrical formula above. Matching unequal impedances needs a “taper pad” with two different series resistor values, derived from separate equations for the input and output arms.
Why choose a T-pad over a Pi-pad?
Both give identical attenuation and matching at the same $Z_0$; the choice mainly comes down to available resistor values and layout — T-pads suit lower shunt resistances, Pi-pads suit higher ones.
How is nepers different from decibels in the output?
The neper is a natural-log-based unit, $\ln(K)$, used in some transmission-line theory; decibels use $\log_{10}$. Both describe the same attenuation, just on different logarithmic scales.
Does resistor tolerance affect the actual attenuation achieved?
Yes. Since R1 and R2 come from exact irrational ratios, standard 1% or 5% resistors shift both the attenuation and the impedance match slightly; precision pads use custom or hand-selected values.