Question

Consider the circuit shown. β₁ = 14 and β₂ = 5. These are small values, so you cannot make any approximation that assumes a large β. Assume both Q₁ and Q₂ are in the forward active mode. Determine the ratio IC₁/IB₂. Enter your answer rounded to the nearest integer.

Vcc
|
R1
|
V1
|
Q1
/ | \
/ | \
/ | \
R2 Q2 Rc
| | |
| | Vout
Re |
| |
Vee |
|
GND

Answer 1

To find the ratio IC₁/IB₂, we use the transistors' current gain values (β), which are 14 for Q1 and 5 for Q2. As IC₁ becomes the base current IB₂ for the second transistor, the ratio simplifies to β1 / β2, yielding an integer ratio of 3.

Step-by-step explanation:

To determine the ratio IC₁/IB₂, we must examine the relationships between the collector current (IC) and the base current (IB) in bipolar junction transistors (BJTs). This ratio is a direct consequence of the transistor's DC current gain (β or 'beta'). Given that β1 = 14 and β2 = 5 for transistors Q1 and Q2, respectively, the relationship for each transistor is β = IC/IB.

For Q1, the collector current IC₁ can be expressed as β1 times the base current of Q1 (IB₁): IC₁ = β1 × IB₁.

For Q2, the collector current IC₂ can be expressed as β2 times the base current of Q2 (IB₂): IC₂ = β2 × IB₂.

However, in a typical cascaded transistor configuration, IC₁ becomes the base current for Q2 (IB₂). Therefore, IC₁ = IB₂. Substituting this into the equation for β2, we get IC₁ = β2 × IC₁ / β1. Simplifying, we find the ratio IC₁ / IB₂ = β1 / β2.

IC₁/IB₂ = β1 / β2 = 14 / 5. Now we can calculate this to get a numerical value which, rounded to the nearest integer, is 3.