Circuits doubt

Question

A small-signal model of an amplifer built using a VCCS (voltage controlled current source), stimulated by a signal source of strength vin, is shown in Figure 8-1.
The device parameters are: RE=1kΩ, RC=10kΩ, rπ =5kΩ, and gm=0.04Ω−1.

What is the voltage gain vout/vin of this amplifier?

What is the input resistance vin/iin in kOhms, seen by the signal source, vin?

 

 

Answer 1

------,b c---------------------------

| | |

Rpi | |

| V gm Vbe Rc

|____e_____| |

| |

Re |

| |

------------G----------------------------------

I don't see Figure 8-1 but it's probably the same as the circuit I've tried to draw above above. The key to solving for the gain and input impedance is to write Kirchhoff's current law (KCL) at node e. This will give you...

Vbe/Rpi + gmVbe = Ve/Re

Kirchhoff's voltage law at the input side gives you

Vin = Vbe + Ve

Combining these two equations

Vin = Vbe (1 + Re/Rpi + gm Re)

At the output we have

Vout=Vc=gm Vbe Rc

From the last two equations, the small signal gain is

Vout/Vin = gmRc/ (1 + Re/Rpi + gm Re) = 400/(1+0.2+40)=9.53

To compute the input impedance, note that the input current is

Iin = Vbe/Rpi

so that

Iin = Vin/(Rpi(1 + Re/Rpi + gm Re))

and

Vin/Iin = Rpi + Re +gm Re Rpi =5K+1K+0.04*1K*5K=206K

If my circuit does not match Figure 8-1, you should be able to use the same method to derive the correct answer.