# In BJT hybrid pi model,why ro resistor is "always" shown even when there is no VCE change.

#### Alim K

Joined Aug 7, 2015
2
In BJT hybrid pi small signal model, we have a resistor "ro" between Collector and Emitter.

This resistor is to include the change in collector current when there is a small signal voltage change between collector and emitter. (due to early effect)

I am finding that all BJT hybrid small signal models keep this "ro" even when there is no
small signal voltage "change" between collector and emitter.

Assume that there is no load resistor between collector and ground. That means always VCC will be maintained between collector and ground.
If Emitter is grounded, then this means that there cannot be any change in voltage between collector and emitter.
"Delta VCE" = 0, means , there cannot be any change in collector current.
As there cannot be any change in collector current, we can avoid this "ro" resistor which
essentially is ( "ro = "Delta VCE"/ "Delta IC" )
In this case why do we include this "ro" resister?

#### Alim K

Joined Aug 7, 2015
2
please assume BJT is biased in the forward active region itself.

Ic = Is {exp(VBE/VT) -1} (1 +VCE/VA)

ΔIc = Is {exp(VBE/VT) -1 } ΔVCE / VA

ro = ΔVCE / ΔIc

if we see hybrid-pi model there is no ΔVCE as part of the model.
that is my doubt. if ΔVCE is not shown, that means ΔVCE = 0.

if ΔVCE = 0 , then ro also must be zero. Am i right?

#### MHDS

Joined May 25, 2015
20
Here the term del(Vce)/del(IC) refers to the hypotenuse of a triangle whose height is equal to Ic & base is equal to VA. And this ro is the hypotenuse of this triangle. Said another way, ro is the inverse of the output characteristics curves. If those curves don't depend upon Vce, their slopes also won't depend upon.

And in an equation, if the nth differentiation doesn't depend upon a quantity, it doesn't mean that the change in that quantity is zero. Rather it's the fact that

#### MHDS

Joined May 25, 2015
20
Rather it means that its (n+1)th differentiation with respect to that quantity will be zero.

#### Brownout

Joined Jan 10, 2012
2,390
ro = ΔVCE / ΔIc

if we see hybrid-pi model there is no ΔVCE as part of the model.
that is my doubt. if ΔVCE is not shown, that means ΔVCE = 0.

if ΔVCE = 0 , then ro also must be zero. Am i right?
No. the ro resistance in the model is there due to intrinsic behavior of transistors. You formula ro = VCE/IC is ohm's law applied to ro, not the definition of ro. The resistor in the model comes about via base width modulation by VCB, and can be defined as r0 = VA/IC, where VA is called the Early Voltage, and is a characteristic of the device. It's always there, even when VCE = 0.

Please see the Early effect: https://en.wikipedia.org/wiki/Early_effect