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Given sinusoidal signal at the input, Find the transfer function for this circuit? Assume that the diodes are ideal.

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0 is less than V_input<5.5 D1 is in forward region and D2 is OFF(b/c V_input-(-V_input)<11, the potential difference between anode and cathode of D2) Hence V_input=V_Output

V_input>5.5 D1 is in forward region and D2 is conducts in Zener region(b/c V_input-(-V_input)>11, the potential difference between anode and cathode of D2), V_output=??

The same happens for the lower half of input with the states of diodes reversing.

Question:

1)I think I have analyzed this circuit incorrectly, where did I go wrong? 2)What is the transfer function for this circuit? 3) is there a systematic procedure to find transfer function of such circuits?

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    \$\begingroup\$ Transfer function is a concept that is normally only applied to linear systems. Your circuit is not a linear system. So to answer the question, we'll have to know what you mean by the transfer function of a nonlinear circuit. \$\endgroup\$ – The Photon Oct 28 '15 at 17:01
  • \$\begingroup\$ I am assuming ideal diodes which have linear relationship for input and output piecewise. By transfer function , I mean how does the output relate to input/What is the waveform of the output? \$\endgroup\$ – Hashir Omer Oct 28 '15 at 17:27
  • \$\begingroup\$ Okay, but the waveform is going to pass through the breaks in the piecewise model. So what do you mean by transfer function for a nonlinear circuit? \$\endgroup\$ – The Photon Oct 28 '15 at 17:39
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    \$\begingroup\$ A full wave rectified sine wave has a strong 2nd harmonic content. As @The Photon says, the system is non-linear and a TF does not exist. \$\endgroup\$ – Chu Oct 28 '15 at 18:17
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    \$\begingroup\$ @HashirOmer You are looking for the "transfer characteristics" and not for the "transfer function" because the latter only applies for linear circuits. \$\endgroup\$ – Roger C. Oct 28 '15 at 19:09
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If Vx is the voltage at the "upper" secondary we'll have -Vx at the "lower" secondary. (You called this the input in your question but the input is in the primary).

If Vx>5.5 then both diodes are ON, one forward and the other in Zener region. The "upper" diode wants Vx at the output, the "lower" wants -Vx+11. Who wins? It depends on the resistance of each path. Assuming diodes ideals and for the transformer equal resistance in upper and lower secondary coils, we have a "tie". Then, assuming this coil resistance much smaller than R_load, the output voltage is simply the average Vo=Vx/2+(-Vx+11)/2=5.5 V.

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