This is a guided problem to help you with diode rectifiers.

• Click here for the circuit simulator for a rectifier using a zero-threshold diode.
• Click here for the circuit simulator for a rectifier using a diode with a threshold.

        Start the first filter simulator - using a zero-threshold diode.  In the simulator, we assume the following.

• The circuit is the one shown below.

• In this circuit, note the following:  (Click here to go to a point in the electronic lessons where this circuit is discussed in more detail.)
• The input is assumed to be a sinusoidal signal.  If you want a square wave signal or a triangular signal, you'll have to look elsewhere.
• Initially, when the input signal is positive, current flows through the diode, D, and some of the current flows into the capacitor, C, charging it, and some of the current flows through the resistor, R.
• When the input voltage signal drops below the voltage on the capacitor current ceases to flow through the diode.  At that point, however, current flows out of the capacitor, through the resistor, discharging the capacitor, reducing the voltage across the capacitor, i.e. reducing the output voltage.  During the discharge part of the cycle, the discharge follows a decaying exponential since the resistor-capacitor circuit is effective de-coupled from the input circuitry because the diode is not conducting.
• As the sine wave cycles through its cycle, it eventually becomes larger than the capacitor voltage, and current again flows through the diode, recharging the capacitor.
• The simulator shows the operation - as described above - starting from zero voltage across the capacitor.  The simulator runs once after you click the Start button..  To re-run, click the Clear button, then click the Start button.

• The value of the DC level is just the average value of the output.  If there were no discharging of the capacitor, then the average value of the output would be the peak level of the input.
• The DC signal that comes out of this circuit is not "pure".  It has a fluctuating component riding on top of the DC level.  One way to specify the level of impurity is to give the Peak-to-Peak value of the fluctuation, i.e. the total range of the fluctuation from the minimum point to the maximum point.

        Run the first simulator (the zero threshold diode) and observe the output.  Before you run the simulator, set the time constant to 50 seconds.  Is the output constant at the peak level of the sine wave?

Question 2

Now, run the first simulator again, but change the time constant to 5 seconds.  Is the output constant at the peak level of the sine wave?

Question 3

Now, answer this question.  What is the peak-to-peak variation in the first signal?

Problem 1

For the second simulation, estimate the peak-to-peak value of the signal.  Don't get fancy, just aim for the closest half of a volt.

• When the current flows through the diode - in the charging portion of the curve - the output voltage is equal to the sinusoidal input voltage because we have assumed that there is no voltage across the diode.  (We assumed a zero threshold.)
• You can estimate the DC voltage output (i.e. the average voltage) by taking the maximum voltage and the minimum voltage and averaging.  This would be the average if both the charging and discharging portions of the output signal curve were straight lines.  However. they are not straight, but they are close enough to being straight that it is a good approximation for what we have done above.

        Re-run the simulator with a time constant of 0.5 seconds keeping everything the same as before.  Examine the curve to determine if a straight line approximation is appropriate, then click on the button of your choice below.

Problem 2

        Now, re-run the simulator with a time constant of 5 seconds and estimate the DC  value (average value) of the output signal.  You might want to check what this button has to say.

        Run the simulator with a time constant of 20 seconds keeping the default values for everything.  How does the peak value change?

• The output voltage does not begin to change (the capacitor does not begin to charge) until the input voltage exceeds the capacitor voltage by the amount of the threshold - which is 0.6 volts in the simulator.
• When the input voltage drops below the capacitor voltage, the capacitor begins to discharge - as before.

        If the capacitor is small, then the time constant becomes small.  Run the first simulator with a very low value of the time constant.  Let's arbitrarily choose a time constant of 0.01 seconds.  Run the simulator.

        Which of these statements is true?

        Run the simulator with a time constant of 0.1  seconds keeping the default values for everything else.  Now, do you see exponential decay?

        Run the second simulator with a time constant of 0.01  seconds keeping the default values for everything else.  Do you see the half sine you saw with the no-threshold simulator?

• The time constant can be critical.  The time constant needs to be substantially longer than the period of the sine wave in order for there to be little "droop" in the output curve.  In practical power supplies that might mean pretty big capacitors, depending upon the load resistor.
• If the time constant is too small, in the limit it might as well not be there since you get the output curve you would get without a capacitor.  The capacitor is necessary for good filtering, i.e. getting a good DC signal out of the circuit.