Diode Circuit Solved Problem (Analog Electronics) | Quiz # 393

Finding Voltage Between Nodes P and Q

Introduction to the Problem

• The video begins with a question about finding the voltage between nodes P and Q at time t = 60 milliseconds, given that all diodes are ideal. The input signal is a sinusoidal wave with a peak value of 10 volts.

Understanding the Signal Characteristics

• The frequency of oscillation is determined to be 50 Hz, leading to a time period of 20 milliseconds. This indicates that each cycle repeats every 20 milliseconds, and we need to analyze the voltage at 60 milliseconds, which corresponds to three cycles.

Diode Behavior During Positive Half Cycle

• During the positive half cycle (0 to +10 volts), the diode conducts as its anode is more positive than its cathode. However, if one diode conducts, it prevents current flow through another diode due to their arrangement in the circuit. Thus, both diodes remain off during this phase.

• The assumption that current can flow through a capacitor is negated because when one diode conducts (acting as a short circuit), both terminals of the capacitor are at equal potential; hence no current flows through it.

• As all four diodes remain off during this half cycle, there’s no current flow affecting node voltages P and Q directly from this phase.

Circuit Behavior During Negative Half Cycle

• In contrast, during the negative half cycle (-10 volts), the bottom diode turns on since its anode becomes more positive than its cathode while allowing current flow through it; however, the upper diode remains off due to reverse polarity conditions preventing conduction.

• Both capacitors charge up to peak voltage (10 volts) during this negative half cycle as they receive current from conducting diodes in their respective paths. This charging behavior establishes critical voltage levels across nodes P and Q for subsequent analysis.

Analyzing Subsequent Cycles

• In subsequent cycles (positive half cycles), node voltages change based on previous capacitor charges: node P's voltage equals input voltage plus 10 volts while node Q remains at -10 volts due to prior conditions established by charged capacitors and non-conducting diodes. Thus:

• Node P varies between 10V and 20V.

• Node Q stays constant at -10V throughout these phases as long as conditions persist unchanged for both nodes' respective diodes being off or on based on input variations from zero to ten volts or vice versa.

Final Observations During Negative Half Cycle

• When transitioning back into another negative half cycle where input polarity changes again:

• Node voltages are reassessed: VP remains influenced by previously charged capacitors while VQ continues reflecting stable values derived from earlier cycles.

• Both lower and upper diodes stay off under these new conditions since neither achieves sufficient forward bias for conduction despite changing input signals.

Thus confirming stability in observed voltages across nodes even amidst alternating cycles of operation within defined parameters set forth initially in problem statement.

Understanding Diode Behavior in Voltage Cycles

Voltage Across Diodes

• The voltage across the lower diode is -10 volts, keeping it in the off condition. Conversely, for the upper diode, the anode voltage is also -10 volts while the other end is at vi.

• During the negative half cycle, as vi varies from 0 to -10 volts, the cathode voltage can reach a maximum of -10 volts. This results in the upper diode remaining off during this phase.

Voltage Relationships

• Throughout subsequent cycles, specifically after three cycles at t = 60 milliseconds, vp equals vi + 10 volts and vq remains at -10 volts. Initially, when vi is 0, vp becomes 10 volts while vq stays at -10 volts.