Chapter 13, Problem 13.1EP

To determine

The currents $I_{\text{REF}},I_{C10},I_{C1}\text{and}{I}_{C2}$ .

Answer to Problem 13.1EP

The currents are:

  $\begin{array}{l}{I}_{\text{REF}}=0.352\text{mA}\\ I_{C10}=16\mu \text{A}\\ I_{C1}=8\mu \text{A}\\ I_{C2}=8\mu \text{A}\end{array}$

Explanation of Solution

Given:

The bias circuit and input stage portion of 741 op-amp circuit is shown below.

  

Figure 1

Resistance $R_5$ is changed from $40\text{k}\Omega$ to $25\text{k}\Omega$ .

Bias voltages are:

  $\begin{array}{l}{V}^{+}=+5\text{V}\\ V^{-}=-5\text{V}\end{array}$

The base current is considered to be 0 A.

The base emitter voltages are:

  $V_{BE\left(on\right)}=V_{EB\left(on\right)}=0.6\text{V}$

Calculation:

Consider the given circuit. The formula for reference current that is established in the circuit branch consists of transistors $Q_{12}$ , $Q_{11}$ and $R_5$ is

  $\begin{array}{c}{I}_{\text{REF}}=\frac{V^{+}-V_{EB12}-V_{BE11}-V^{-}}{R_5}\\ =\frac{5-0.6-0.6-\left(-5\right)}{25\times {10}^3}\\ =\frac{10-1.2}{25}\times {10}^{-3}\\ =\frac{8.8}{25}\times {10}^{-3}\\ =0.352\times {10}^{-3}\\ =0.352\text{mA}\end{array}$

Transistors $Q_{11}$ , $Q_{10}$ and resistor $R_4$ form a Widler current source. So, a current $I_{C10}$ is given as,

  $I_{C10}{R}_4=V_T\ln \left(\frac{I_{REF}}{I_{C10}}\right)$

Where,

  $V_T$ is the thermal voltage and it is equal to 0.026 V.

Substitute the given values in the above equation.

  $I_{C10}\left(5\times {10}^3\right)=0.026\times \ln \left(\frac{0.352\times {10}^{-3}}{I_{C10}}\right)$

By trial and error method,

  $I_{C10}=16\mu \text{A}$

For the given circuit, if the base current is neglected, then the collector current through transistors $Q_8$ , $Q_9$ and $Q_{10}$ will be same while the collector current in transistor $Q_1$ through transistor $Q_4$ will be

  $I_{C1}=I_{C2}=I_{C3}=I_{C4}=\frac{I_{C10}}{2}$

Substituting the values,

  $\begin{array}{c}{I}_{C1}=I_{C2}=\frac{I_{C10}}{2}\\ =\frac{16\times {10}^{-6}}{2}\\ =8\times {10}^{-6}\\ =8\mu \text{A}\end{array}$