Basic circuit with diodes analysis

Question

I have the following circuit:

How to determine the waveform of Vout, maximum values for positive and negative half-period segments, and the average value of Vout?

Input voltage Vin has a sinusoidal signal of frequency 1kHz and amplitude 10V. Diodes are ideal.

Answer 1

Firstly consider the DC operating point of the circuit.

Vout is the sum of the voltage drop over the 1k resistor and the voltage drop over the silicon diode = 1k * 1mA + 0.53V = 1.53V. (The voltage drop over a silicon diode will be ~0.53V at 1mA).

Now consider the effect of Vin. Diode D2 places an upper limit on Vout (1.53V) and an upper limit of 0.53V on the node where the diodes connect. Using a mathematically idealized model for the diode, it holds that if Vin > 0, the voltage drop over D1 cannot be 0.53V, and D1 will be reversed biased, i.e. Vin has no effect.

However, if Vin < 0, D1 will be forward biased and will pull down the voltage at Vout, Vout = Vin + 1.53V. D2 will be reversed biased and will have no effect.

So the maximum value for Vout = 1.53V and the minimum = -8.47V.

Using the idealized model for the diode we have a half-wave rectified sine with a -10V peak and a 1.53V offset. The average for a half-wave rectified sine is Vpeak/pi, so in this case -10/pi + 1.53 = -1.65 V

Answer 2

Notice a few constraints:

1. If Vout is unloaded (left open), then it will always be 1 V higher than the tops of the diodes.

2. D2 causes the tops of the diodes to always be ≤0 V.

3. D1 causes the tops of the diodes to always be ≤ Vin.

Put these together to determine the overall characteristics. This is really pretty easy.