Question

Which of the following represents the correct relationship between collector to emitter cut-off current (I_CEO) of a transistor and collector to base cut-off current (I_CBO)?

(Assume: 'x' is the CB current gain of the transistor)

1. I_ECO = I_CBO
2. IECO = x ⋅ I_CBO
3. IECO = I_CBO/(1 - x)
4. IECO = I_CBO/ (1 + x)

Answer 1

Correct Answer - Option 3 : IECO = I_CBO/(1 - x)

Expression of Collector current in CE configuration:

In CE configuration, IB is input current and I_C is output current.

We know that,

I_E = I_B + I_C …. (1)

In CB cofiguration, The expression of collector current is written as,

I_C = xI_E + I_CBO …. (2)

From equation (1) and (2),

I_C = x (I_B + I_C) + I_CBO

I_C (1 – x) = αI_B + I_CBO

 \(I_C=\frac{x}{1-x}I_B+\frac{1}{1-x}I_{CBO}\)…. (3)

From equation (3), it is apparent that if I_B = 0, the collector current will be equal to the collector to emitter cut-off current (ICEO).

This is abbreviated as I_CEO, meaning Collector-Emitter current with base open.

∴IECO = ICBO/(1 - x)