Today's lecture focuses on two diode circuits: Halfwave Rectifier and Fullwave Rectifier.
Emphasis on understanding input-output characteristics and time response to determine how circuits behave with time-varying signals.
Halfwave Rectifier
Composition: A diode (D1) and resistor (R1).
Functionality:
If input voltage is negative, D1 is off, resulting in zero output.
The diode turns on when input voltage exceeds the forward voltage drop (V_D_on).
Output voltage essentially tracks input minus the diode drop (V_D_on) when the diode is on.
Behavior with Sinusoidal Input:
At low input voltages, diode remains off and output is zero.
After input voltage exceeds V_D_on, output mirrors the input minus V_D_on until the input goes lower than this threshold.
Output remains at zero during negative input cycles.
Waveform Characteristics:
Produces a rectified waveform with positive cycles of the input signal only (i.e., half of the waveform).
Smoothing Capacitor Application
Issue: The output waveform fluctuates, which is not ideal for powering devices.
Solution: Adding a capacitor (C1) at the output from D1 instead of a resistor, which helps stabilize the voltage by smoothing out fluctuations due to charging and discharging.
Operation:
During positive cycles, when the diode turns on, the capacitor charges.
Once capacitor voltage stabilizes, it ideally maintains a constant output as long as the input doesn’t drop significantly below this voltage.
Time Response Analysis of Halfwave Rectifier with Capacitor
Charging Phase: When the diode conducts, the output voltage increases until it reaches a peak determined by V_in - V_D_on.
Discharging Phase: When input voltage decreases and the diode is off, the capacitor discharges through the load.
Ripple Effect: This leads to ripple characteristics, where voltage decreases exponentially, reflected in the output.
This ripple causes undesirable fluctuations in DC output.
Calculation of Ripple:
Define Ripple Amplitude (R) as the difference between the maximum output and minimum output during discharge.
Formulation for Ripple:
R = (V_0 - V_D_on)(T_In / tau)
Where T_In is the period of the input waveform and tau is the time constant (R1*C1).
Design Considerations
Components:
Choose R1 / C1 carefully to minimize ripple in case of increased load current demands.
Consider the maximum reverse voltage the diode must withstand; it should be above the breakdown voltage.
Understand the role of R1 in defining output voltage when the diode is off, providing a reference circuit condition.
Conclusion
The proper design and understanding of the halfwave rectifier with smoothing capacitor allow for efficient conversion from AC input to usable DC output, albeit with inherent ripple characteristics.
Next Steps
Move on to the analysis of the Fullwave Rectifier in the next lecture.