What is the reflected impedance to the primary Z_ref in terms of turns ratio and load Z_load?

What is the reflected impedance to the primary Z_ref in terms of turns ratio and load Z_load?

• A. Z_ref = Z_load
• B. Z_ref = (N_s/N_p)^2 Z_load
• C. Z_ref = (N_p/N_s)^2 Z_load
• D. Z_ref = (N_p/N_s) Z_load

Answer: (C)

When you look into the primary of an ideal transformer, any impedance connected on the secondary side appears as a different impedance on the primary, scaled by the square of the turns ratio. If the primary has Np turns and the secondary has Ns turns, and the load on the secondary is Z_load, then the impedance seen from the primary is Z_ref = (Np/Ns)^2 Z_load. You can see this from the transformer relationships: Vp = (Np/Ns) Vs and Ip = (Ns/Np) Is for an ideal transformer. The impedance seen from the primary is Z_ref = Vp/Ip = [(Np/Ns) Vs] / [(Ns/Np) Is] = (Np/Ns)^2 (Vs/Is) = (Np/Ns)^2 Z_load. So the reflected impedance scales with the square of the turns ratio. For example, if Np/Ns = 2, a 10 Ω load on the secondary reflects as 40 Ω on the primary.

When you look into the primary of an ideal transformer, any impedance connected on the secondary side appears as a different impedance on the primary, scaled by the square of the turns ratio. If the primary has Np turns and the secondary has Ns turns, and the load on the secondary is Z_load, then the impedance seen from the primary is Z_ref = (Np/Ns)^2 Z_load.

You can see this from the transformer relationships: Vp = (Np/Ns) Vs and Ip = (Ns/Np) Is for an ideal transformer. The impedance seen from the primary is Z_ref = Vp/Ip = [(Np/Ns) Vs] / [(Ns/Np) Is] = (Np/Ns)^2 (Vs/Is) = (Np/Ns)^2 Z_load.

So the reflected impedance scales with the square of the turns ratio. For example, if Np/Ns = 2, a 10 Ω load on the secondary reflects as 40 Ω on the primary.