To design an SCR rectifier circuit with an average output voltage of 77.64V, we need to determine the appropriate circuit components and calculate their values.

Here is a step-by-step guide to designing the SCR rectifier circuit:

Step 1: Determine the average output voltage
Given that the average output voltage is 77.64V, we will consider this as the DC output voltage. The peak voltage of the AC input will be higher than this value due to the rectification process.

Step 2: Determine the peak voltage
The peak voltage (Vp) is related to the average output voltage (Vdc) by the following equation:
Vp = Vdc * √2

Substituting the given value, we get:
Vp = 77.64V * √2 ≈ 109.84V

Step 3: Choose the load resistance
Select the load resistance (RL) based on the desired load current and the available power supply. The load resistance determines the current flowing through the circuit.

Step 4: Calculate the peak current
The peak current can be determined using the peak voltage and the load resistance:
Ip = Vp / RL

Step 5: Select an appropriate SCR
Choose an SCR (Silicon-Controlled Rectifier) that can handle the calculated peak current (Ip). Check the datasheet of the SCR to ensure it can handle this current rating.

Step 6: Calculate the trigger angle
The trigger angle (α) determines when the SCR is turned on during each half-cycle of the AC input voltage. The trigger angle is usually specified in degrees.

Step 7: Determine the firing circuit
Design and implement a firing circuit to trigger the SCR at the desired trigger angle (α). This can be achieved using various methods such as voltage triggering, current triggering, or pulse triggering.

Step 8: Design the power supply
Design a power supply that can provide the required voltage and current to the SCR and load. This may involve using a transformer, rectifier diodes, and smoothing capacitors to convert the AC input voltage to the desired DC output voltage.

Step 9: Test and verify
Once the circuit is designed and implemented, test and verify its performance. Make any necessary adjustments or modifications if required.

Note: The above steps provide a general guideline for designing an SCR rectifier circuit. The specific circuit configuration and component values may vary depending on the application requirements and constraints.