How to use the Two-Port Network Parameters Calculator
- 1. Choose what you knowZ, Y, h, g, ABCD, a T network or a π network.
- 2. Enter four valuesReal or complex, such as 4, 2+j3 or 5∠30.
- 3. ConvertSee every set, its formula and the reciprocity check.
Two-port parameters and conversions
A two-port network relates V1, I1, V2 and I2. Each parameter set picks two of them as outputs. Z: V1 = Z11I1 + Z12I2 and V2 = Z21I1 + Z22I2. Y: I = YV. h: V1 = h11I1 + h12V2 and I2 = h21I1 + h22V2, which is used for transistors. ABCD: V1 = AV2 − BI2 and I1 = CV2 − DI2, which is used for cascaded networks and transmission lines. The conversions use the determinant, for example Y11 = Z22/ΔZ and A = Z11/Z21.
Worked example: Z11 = 4, Z12 = Z21 = 2 and Z22 = 6 Ω give ΔZ = 24 − 4 = 20. Then Y = [0.3, −0.1; −0.1, 0.2] S, h11 = 20/6 = 3.333 Ω, h12 = 0.333, h21 = −0.333, h22 = 0.1667 S, and ABCD = 2, 10 Ω, 0.5 S, 3. AD − BC = 6 − 5 = 1, so the network is reciprocal.
Exam tips
- Reciprocal networks have Z12 = Z21, Y12 = Y21, h12 = −h21 and AD − BC = 1.
- Symmetric networks also have Z11 = Z22 and A = D.
- For networks in cascade, multiply the ABCD matrices. For networks in series, add Z. For networks in parallel, add Y.
- Some sets do not exist: a single series impedance has no Z parameters, and a single shunt impedance has no Y parameters.
Frequently asked questions
Which sign convention is used?
Both port currents flow into the network. ABCD uses −I2, the current leaving port 2, which is the usual textbook convention.
Why does a parameter set show 'does not exist'?
The conversion needs to divide by a determinant or element that is zero for this network. For example, a pure series impedance has C = 0, so its Z parameters do not exist.
Can I use complex impedances?
Yes. Every value can be complex, such as 2+j3 or 5∠30, so the tool also works for AC networks.
Is this tool free?
Yes. You fill in a short form once to see your result, and the other Uncodemy tools then open without it. All the maths runs in your browser.