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Input Resistance of a BJT with collector-to-base feedback resistor

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Electric Mick

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Hello,

I need to calculate the input resistance of a Bipolar Transistor with a resistor from collector to 20V (R1) and a resistor from base to collector (R2). Any idea how I should go about doing so? I have tried looking at small signal circuit analysis but this has failed to yield the correct answer.

Thank you
 
Hello,

I need to calculate the input resistance of a Bipolar Transistor with a resistor from collector to 20V (R1) and a resistor from base to collector (R2). Any idea how I should go about doing so? I have tried looking at small signal circuit analysis but this has failed to yield the correct answer.

Thank you

Hi,

I am not sure if you just need to do this one time or you want to know some theory of how to do this mathematically.
If you take Nigel's advice you can use build the circuit in spice to simulate, then do a few tests to determine the input resistance.
If you want a straight up mathematical analysis you can assume that the transistor is a controlled current source, then perform a few math tricks to get the result. This usually involves assuming a range of Beta values for the transistor just like other calculations that involve bipolar transistors.
The transistor, when viewed as a constrained current source, leads to a circuit which is fairly simple with only two nodes so it's not hard to calculate.
However, you'd also have to have knowledge of the base emitter diode IV curve.
 
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Using Thevenin equivalent circuits, build it. Put a 1K (for example) in series with the output of your test circuit (say 10mV). Load it with your circuit and measure the new input voltage between your 1K resistor and the input circuit. The drop in input voltage will be caused by the loading impedance. The rest is school boy maths.

Image2.jpg
 
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Hello again,

One way to do this is to look up the curve for the transistor in the data sheet. We can then solve for the diode parameters N and Iss in:
Ib=Iss*e^(Vbe/(N*VT))

The collector current is then:
Ic=Ib*Beta

and with a base resistor Rb from Vin to base, collector resistor Rc from collector to Vs, and feedback resistor Rf from collector to base the circuit equation for the base current is:
Ib=(Vin-Vb)/Rb+(Vc-Vb)/Rf

and the collector voltage is:
Vc=Vs-Ic*Rc

Combining those equations we come out with a single equation:
-Vs-(Rf*Vin)/Rb+(Rf*Vbe)/Rb+Vbe+e^(Vbe/(N*VT))*Iss*Rf+Beta*e^(Vbe/(N*VT))*Iss*Rc=0

We then perturb this by changing Vin to two different levels that are not too different, and calculate Vbe for each level. We get two solutions we'll call simply Vbe1 and Vbe2. Inserting those solutions into the exponential equation for the base current, we get two base currents we'll call simply Ib1 and Ib2, respective to each Vbe. We can then calculate the input resistance as:
Rin=(Vbe2-Vbe1)/(Ib2-Ib1)

This is still an estimate and of course it may change a little depending on what the value of Rb is as that is the resistance we might see in the output of the previous stage. It will also change depending on the other resistors of course, and even the level of the power supply voltage Vs. So it is just an estimate and subject to change depending on the other changes in circuit components and power supply.

A typical value found with N=1.37 and Iss=1e-12 and VT=0.026 and Rb=10k and Rc=1k and Rf=100k was Rin=around 400 Ohms. This will vary with the type of transistor too as N and Iss will change, and so will the ambient temperature.
 
Hello,

I need to calculate the input resistance of a Bipolar Transistor with a resistor from collector to 20V (R1) and a resistor from base to collector (R2). Any idea how I should go about doing so? I have tried looking at small signal circuit analysis but this has failed to yield the correct answer.

Thank you

This is the homework help forum, and the forum members will be better able to help you if you give full information about your problem, and show your attempt to solve the problem.

You say that you tried small signal circuit analysis. If you show your work then it should be possible to determine where you went wrong.
 
Hi,

Looks maybe like another fly by night poster who happened by, asked a quick question, then disappeared into the night never to be seen or heard from again :)
 
input resistance is a property of small-signal analysis, NOT large-signal/DC bias analysis.

draw the small-signal equivalent circuit, then attach a test source (vt) at the input, write the node (or mesh) equations, and solve for vt/it to get Rin.
 
Hi there lebevti,

Well, there are actually two approaches...the small signal approach and the large signal approach...and they will both give the same result. The large signal approach depends on the large signal change in voltage dv and change in current di, the differentials. So it ends up looking something like dv/di.
 
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