Zener voltage controlled circuit design

[bl965]

Homework Statement

Homework Equations

V₀=V_sr_z/R_s+r_z+V_zoR_s/R_s+r_z-I_Lr_zR_s/r_z+R_s

The Attempt at a Solution

I formulated 4 cases for voltage inputs of 11 and 13.6 V and 0 to 100 mA. The zener current has to be between 3 and 30mA or 103 and 133mA. How can the current be maintained in thes two ranges? does the diode stop conducting?
Thank you.

 

[QuantumQuest]

I formulated 4 cases for voltage inputs of 11 and 13.6 V and 0 to 100 mA. The zener current has to be between 3 and 30mA or 103 and 133mA. How can the current be maintained in thes two ranges? does the diode stop conducting?
Thank you.

Take some extra care about the distinction between current passing through zener diode and current through radio. What rule do you have to apply? Which current value (min vs. max), considering both branches (zener - load), are you interested in, in order to conclude about what is asked?

 

[bl965]

Take some extra care about the distinction between current passing through zener diode and current through radio. What law do you have to apply? Which current value (min vs. max) considering both branches (zener - load) are you interested in in order to conclude about what is asked?

The current law must be obeyed. If the radio does not draw the current it must pass through the zener. How can this be possible if the zener cannot handle more than 30 mA?

 

[LvW]

Homework Equations

V₀=V_sr_z/R_s+r_z+V_zoR_s/R_s+r_z-I_Lr_zR_s/r_z+R_s

Did you forget some brackets in this equation? It cannot be read at all.
It looks as if you add a voltage to a resistance .

 

[QuantumQuest]

The current law must be obeyed. If the radio does not draw the current it must pass through the zener. How can this be possible if the zener cannot handle more than 30 mA?

If radio does not draw any current, what is the equivalent resistance of the circuit? Is the value of the current staying unchanged?

 

[bl965]

If the radio does not draw any current, than the circuit is the battery, the resistor and the Zener. The current would not change. When learning forward bias diode voltage regulation, when the load changes current, that change is added or removed from the diode and the change in voltage is calculated as current times r_d, but in this problem r_z is not given. How is r_zcalculated?

 

[bl965]

Did you forget some brackets in this equation? It cannot be read at all.
It looks as if you add a voltage to a resistance .

V₀=V_sr_z/(R_s)+r_z+V_zoR_s/(R_s+r_z)-I_Lr_zR_s/(r_z+R_s)

 

[QuantumQuest]

If the radio does not draw any current, than the circuit is the battery, the resistor and the Zener. The current would not change. When learning forward bias diode voltage regulation, when the load changes current, that change is added or removed from the diode and the change in voltage is calculated as current times rd, but in this problem rz is not given. How is rzcalculated?

I'll state what I previously said, in another way. Take Ohm's Law. Suppose you have the same car battery. If you change the total resistance of the circuit in no matter what way, does the current stay unchanged?

EDIT: After the answer to this, think about zener, what it achieves and how regarding Ohm's Law.

 

[NascentOxygen]

does the diode stop conducting?

The zener must be conducting at all times, otherwise the circuit is not regulating. Here, you are told that the zener current must at all times be at least 3mA. That's its minimum; and the zener current will jump to a high value when the load is switched off.

The calculations are simplified in this question because you can consider r_z = 0 Ω

 

[NascentOxygen]

How can this be possible if the zener cannot handle more than 30 mA?

Now right there we have a problem. [emoji79]

It looks like a mistake in their specs for the Zener, if we assume R_L is supposed to be representing the radio---in which case you'll have to ignore what they imply is I_Zmax

 

[David Lewis]

When learning forward bias diode voltage regulation, when the load changes current, that change is added or removed from the diode and the change in voltage is calculated as current times rd,

But the resistance of a diode (rd) operating in the breakdown region varies. The voltage drop will be fairly constant over the design range of diode current.

 

[NascentOxygen]

r_d being the Zener's incremental resistance at the operating point