Designing a Bias Circuit for BJT with Optimal Ratio and Voltage Drop

In summary: So, you can get (RB/RE)max and then simply multiply it by the required Ie.In summary, To design the bias circuit for a BJT with β=100, the largest ratio (Rb/Re) that guarantees Ie to remain within 10% of its nominal value for B as low as 50 and as high as 150 is 0.1022. This is determined using the stability equation S=1.1=51(1+(Rb/Re))/(51+(Rb/Re)). Additionally, the voltage Vbb can be calculated using the formula Vbb=RE*IE(1+Rb/(RE*(β+1)))+0.7. Another method to find
  • #1
lisp
1
0

Homework Statement


It is required to design the bias circuit as shown in figure for a BJT whose nominal [tex]{\beta} [/tex] is 100.
upload_2015-2-8_13-37-21.png
upload_2015-2-8_13-37-43.png
a.) Find the largest ratio [tex]{(R_B/R_E)}[/tex] that will guarantee [tex]{I_E}[/tex] remains within 10% of its nominal value for B as low as 50 and as high as 150.

b.) If the resistance ratio found in a.) is used, find an expression for the voltage [tex]{V_(bb) = V_(cc) *(R_2/(R_1+R_2)) }[/tex] that will result in a voltage drop of [tex]{V(cc)/3}[/tex] across [tex]{R_E}[/tex].

Homework Equations



[tex]V(bb) = V(cc) * (R2/ (R1+R2))[/tex]
[tex]Rb = R1*R2 / (R1+R2)[/tex]

The Attempt at a Solution



a.) Using the stability factor equation found somewhere else (not sure if it is a relevant equation).

[tex] S = (1+\beta) (1+ (R_B/R_E))/(1+\beta+(R_B/R_E)) [/tex]

For largest ratio, [tex]{\beta}[/tex] is low and S is high.

[tex] 1.1 = 51 * (1+(R_B/R_E))/(51+(R_B/R_E)) [/tex]
[tex] R_B/R_E = 0.1022 [/tex]

b.)
[tex] V_(bb) - R_B*I_B-0.7-I_E*R_E = 0 [/tex]
[tex] V_(bb) = R_B* (I_E)/(B+1) + 0.7 + V_(cc)/3 [/tex][/B]
 

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  • #2
lisp said:
b.)
V(bb)−RBIB−0.7−IERE=0​
Hi lisp. http://img96.imageshack.us/img96/5725/red5e5etimes5e5e45e5e25.gif

You might be able to use this approach:

Vbb = RB*IE/(β+1) + IE*RE + 0.7

= RE*IE (1 + RB/(RE(β+1))) + 0.7

A decision has to be made: what value to use for β?

Can you post a link to the derivation of the Stability Factor? That might assist someone who may be able to help with that question.

P.S. with the name "lisp", you should be comfortable with lots of nested parentheses!
 
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  • #3
Hi lisp,

I don`t know where your stability formula comes from. Nevertheless, I have used another formula in ealier times, involving simply the max and min values for Ic~Ie:

K=Ic,max/Ic,min=(Numerator N)/(Denominator D) with
N=[(1+B1)/B1 + RB/RE*B1] and D=[(1+B2)/B2 + RB/RE*B2]
with B1=Bmin and B2=Bmax.

Now you can solve for (RB/RE)max. if you know the value of K.
Based on the given 10% Ic variation we have K=(1+0.1)/(1-0.1)=1.222.
 
Last edited:

Related to Designing a Bias Circuit for BJT with Optimal Ratio and Voltage Drop

1. What is a bias circuit?

A bias circuit is a circuit that is used to set the operating point, or quiescent point, for an electronic device, such as a transistor or amplifier. It provides a stable DC voltage or current to ensure the device operates in its desired range.

2. Why is a bias circuit necessary?

A bias circuit is necessary to ensure the stability and proper functioning of electronic devices. Without a bias circuit, the device may operate in an unstable or inefficient manner, leading to distortion or malfunction.

3. What are the different types of bias circuits?

The three main types of bias circuits are fixed bias, self-bias, and voltage-divider bias. Fixed bias uses a fixed DC voltage to set the operating point, self-bias uses the device's own characteristics to establish the operating point, and voltage-divider bias uses a voltage divider circuit to set the operating point.

4. How do you design a bias circuit?

The design of a bias circuit depends on the specific electronic device and its desired operating point. The design process involves selecting the appropriate type of bias circuit, calculating the necessary values for the components, and testing the circuit to ensure proper functioning.

5. What are some common issues with bias circuits?

Common issues with bias circuits include thermal stability, which can cause the operating point to shift with temperature changes, and sensitivity to variations in power supply voltage. These issues can be addressed through careful component selection and circuit design.

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