Question
Draw the circuit diagram of a full wave rectifier using two diodes and a centre-tapped transformer. Explain its working and show that the output frequency is twice the input AC frequency.
Solution — Step by Step
We use a centre-tapped transformer with its secondary coil split into two equal halves. Diode D₁ connects to the top end, Diode D₂ to the bottom end, and the centre tap acts as the common ground reference. The load resistor connects between the two diodes’ cathodes and the centre tap.
During the positive half cycle, the top of the secondary is at higher potential. D₁ is forward biased (its anode is positive), so it conducts. D₂ is reverse biased simultaneously because the bottom of the secondary is at lower potential — current flows through D₁ → → centre tap.
During the negative half cycle, the polarity flips. Now the bottom of the secondary is at higher potential, so D₂ is forward biased and conducts. D₁ is now reverse biased. Current again flows in the same direction through — from cathode side to centre tap. This is the key insight: both halves push current through in the same direction.
The input AC has frequency , so its time period is . D₁ gives one output pulse per full cycle, and D₂ gives another pulse in the same cycle. So we get two output pulses per input cycle. Output frequency . If input is 50 Hz mains supply, output pulsating DC has frequency 100 Hz.
The ripple factor for a full wave rectifier is , compared to 1.21 for a half wave rectifier — this is why full wave rectification is practically preferred. The rectification efficiency is approximately 81.2%, double that of a half wave circuit.
Why This Works
The centre tap is the clever trick here. By splitting the secondary into two equal halves and using it as the reference point, we effectively create two separate AC sources that are 180° out of phase with each other.
When one source drives D₁ on the positive swing, the other source is simultaneously negative — which forward biases D₂ on the next half swing. The load sees a continuous flow of current because there is never a dead period. This is fundamentally different from a half wave rectifier where the load only receives current for half the time.
Alternative Method — Bridge Rectifier (for comparison)
A bridge rectifier achieves the same full wave rectification using four diodes instead of two, but without needing a centre-tapped transformer. In the positive half cycle, diodes D₁ and D₃ conduct; in the negative half cycle, D₂ and D₄ conduct. The output frequency is still .
CBSE boards frequently ask you to compare these two. The centre-tap circuit uses fewer diodes (2 vs 4) but wastes half the transformer secondary voltage at any instant — peak output is , not . The bridge rectifier uses the full secondary voltage: peak output is (since no centre tap is needed).
The choice in exam questions: if they say “centre-tapped transformer,” draw the two-diode circuit. If they say “bridge rectifier,” draw all four diodes in the diamond configuration.
Common Mistake
Students often say “both diodes conduct simultaneously.” This is wrong — only one diode conducts at a time. D₁ is on when D₂ is off, and vice versa. If both conducted at once, you’d have a short circuit across the secondary winding. In your diagram, always show the reverse-biased diode clearly, or the examiner will dock marks.
Another slip: forgetting that the PIV (Peak Inverse Voltage) rating for each diode must be at least in this circuit — because when D₁ conducts, D₂ sees the full voltage across both halves of the secondary. This appeared as a 2-mark numerically in CBSE 2023.