Range of values of Vi that will maintain the zener diode in the on state

The zener diode is a special type of diode that is designed to operate in the reverse breakdown region. When the voltage across the zener diode exceeds a certain value called the zener voltage (Vz), the diode starts conducting in the reverse direction and maintains a nearly constant voltage across its terminals.

To maintain the zener diode in the on state, the voltage across the diode (Vd) should be greater than or equal to the zener voltage (Vz). This can be achieved by controlling the input voltage (Vi). Let's analyze the different scenarios to determine the range of values for Vi.

1. Vi < />
When the input voltage (Vi) is less than the zener voltage (Vz), the zener diode will be in the off state. In this case, the diode acts as an open circuit and no current flows through it.

2. Vi = Vz
When the input voltage (Vi) is equal to the zener voltage (Vz), the zener diode just starts conducting in the reverse direction. The diode is in the on state, and the voltage across it remains constant at Vz.

3. Vi > Vz
When the input voltage (Vi) is greater than the zener voltage (Vz), the zener diode is in the on state, and it maintains a constant voltage of Vz across its terminals. The excess voltage (Vi - Vz) appears across the series resistor (Rs) in the circuit.

To calculate the range of values for Vi that will maintain the zener diode in the on state, we need to consider the maximum current (Iz) that the zener diode can handle without getting damaged. This maximum current is given by the zener diode's datasheet.

Using Ohm's law, we can calculate the maximum allowable input voltage (Vi) as:
Vi_max = Vz + (Iz * Rs)

In this equation, Rs is the series resistor connected in series with the zener diode to limit the current through it. The value of Rs is determined based on the desired current (Iz) and the input voltage (Vi) according to Ohm's law:
Rs = (Vi - Vz) / Iz

By substituting the value of Rs in the equation for Vi_max, we can calculate the maximum allowable input voltage (Vi).

Therefore, to maintain the zener diode in the on state, the input voltage (Vi) should be greater than or equal to the zener voltage (Vz). The maximum allowable input voltage (Vi_max) is determined by the zener voltage (Vz) and the maximum current (Iz) that the zener diode can handle.