Transformers: Turns ratio, voltage ratio and current ratio
Transformers: Turns ratio, voltage ratio and current ratio
If there are N1 turns on the primary of a transformer and N2 turns on the secondary we observed that the ratio of voltages V2/V1 is approximately N=N2/N1 but that the ratio of currents I2/I1 is not 1/N. What’s up?
Here is the circuit that we used.
[pic]
In the lab the value of the resistor in the secondary is R = 10 ohms.
The equations governing the transformer are given in the ECE 0031/0041 text (Dorf 7th edition page 523, 8th edition page 523. There are several sign differences, due to the direction of coupling, between the paragraphs below and those used in the 8th edition of Dorf).
The governing equations are
v1 = L1 di1/dt - M di2/dt
v2 = - L2 di2/dt + M di1/dt
where L1 and L2 are the inductances of the primary and secondary and M is the mutual inductance. M = k [L1L2]1/2 and k is a coupling coefficient 0>R/N2 then i1 = v1N2/R
or (from equation 3) i2/i1 = 1/N.] For most transformers (but not for the transformer in the lab) this inequality is satisfied. For the lab experiment ω L1 = 2π (400 Hz) 0.01 H = 25 ohms and R/N2 is approximately 10/ 0.16662 = 360 (60 turns on primary, 10 turns on secondary) and the inequality is not satisfied. There is a simple physical interpretation to Eq. (4). The primary current has two components; one is due to the load; one is due to the inductance of the primary winding. We can view the load (reflected to the primary) and the primary inductance as elements in parallel and equation (4) is then a statement of KCL. If the inductance of the primary is large, the equations reduce to those that we anticipated.
Pspice has the capability of modeling a transformer where the inductances of the windings are small. Our transformer can be accurately modeled in Pspice.
Mike Gorham, a student in ECE 1201 a few years ago, took a picture of primary voltage (trace one), primary current (trace 2) and secondary voltage (trace 3) for the transformer that he made in the lab. The picture is copied below.
[pic]
Notice that the primary and secondary voltages are in phase and that the primary current (actually the voltage across a small resistor in the primary circuit) is not in phase with these voltages.
File updated (typos corrected): November 20, 2006, update November 26, 2007. Update of references to Dorf, November 28, 2011, correction to equation 4 November 28, 2011
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