Dynamic resistance of zener diodes

Thread Starter

HarrisonG

Joined Aug 1, 2016
73
I am trying to give myself a physical explanation of the dynamic resistance in zener diodes. This is what I made up:
We know that zener's dynamic resistance Zzt is verry large for small currents and small for high currents. So here, starting forth to back, I speculate. When will the current be low? --> when the input voltage is small. When will the current be high? --> when the input voltage is high. And from here I get, that as soon as you apply Vtreshold the zener breakdown occurs and minimal zener voltage flows. At that point the resistance is pretty big (500ohms in some diodes). As you increase the input voltage, you turn it on even harder, the resistance decreases and the current goes up. And so at Izt, Zzt will be verry small. And from here it becomes clear to me why there is much bigger change in Vz at lower currents than at the test current.
Is that right?
 

Thread Starter

HarrisonG

Joined Aug 1, 2016
73
Static resistance is the ordinary ohmic resistance that resistor have. Its caused by the resistive nature of the material. As for Dynamic resistance, its the non linear relation between I and V. Non linear because R=V/I no longer applies to that. The new formula is R=dV/dI. Ive heard in pn junctions, dynamic resistance can be caused by transition or diffusion capacitances.
 

Jony130

Joined Feb 17, 2009
5,488
I do not like your definition.
Static resistance (capital R) is the ratio of the DC (Q - point) voltage across a device to the DC (Q-point) current through the device.
Dynamic resistance (lowercase r) is the ratio of the change in voltage across a device to the change in current through the device.

And for example if we plot V-I characteristic for a 100Ω resistor we well get this:

1.pmg.png

In the case of a resistor, we simply divide the voltage across it by the current through it . We see that at any point on its V-I curve, the resistance
is a constant. Specifically, we see that 1 V/10 mA = 100Ω or 2 V/20 mA = 100Ω.
So the Static resistance is 100Ω. But what about a Dynamic resistance ?
Let us see r = ΔU/ΔI = (2V - 1V)/(20mA - 10mA) = 1V/10mA = 100Ω. So far so good, nothing new here.
But the resistance of a resistor is constant for two reasons:
First, the V-I characteristic is linear, and second, the V-I characteristic passes through zero.
Both of these constraints must hold true for the resistance to be a constant.

But what if we add a voltage source in series with a 100Ω resistor and we closed it into the black box. So we crate a new two terminal device.
And now we plot the V-I characteristic for our new device closed in the black box.
And the result is:

2.png

The curve is still linear, but it is offset from zero. So now let us try to find a Static resistance.
For Vin = 2V we have a current of 10mA, at 3V we have a current of 20 mA, and at 4V the current is 30 mA. 30mA
If we divide these voltages by their corresponding currents we obtain :

R = 2V/10mA = 200Ω
R = 3V/20mA = 150Ω
R = 4V/30mA = 133Ω

As you can see the Static resistance is no longer constant.

The reason the resistance appears to change is because we are finding the total resistance offered by the resistor and voltage source combination.
What we have found is the DC (static) resistance at three particular operating points and Ohm's law is still valid.

What about the Dynamic resistance for our new device in black box?

r = (3V - 2V)/(20mA - 10mA) = 100Ω
r = (4V - 1V)/(30mA - 0mA ) = 100Ω
r = (4V - 0V)/(30mA - (-10mA)) = 100Ω

As you can see the dynamic resistance is constant and equal to 100Ω. So for AC signal our new device in a black box behaves just like a 100Ω resistor.
 
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