C.1. DC (Bias) Analysis

The two common-emitter amplifier-stage configurations studied in projects are shown in Fig. C.1. We note that the dc circuit of Fig. C.1(a) is that of Fig. B.12. Amplifier performance analysis can be performed with the two output channels available from the DAQ in the following manner: Fig. C.1(a) uses separate channels for the input and output bias circuits and superimposes the input signal on the input bias. In Fig. C.1(b) we add a signal-source resistor and coupling capacitor and use one channel for the input signal and one channel for bias. The capacitor is required to prevent the connection of the signal source from affecting the dc (bias) operation of the circuit. The latter represents the classical practical common-emitter amplifier stage. The signal-source resistor provides for a current-source input signal and hence linear amplification.

In the experimental project on the common-emitter amplifiers, we measure the voltage gain as a function of the collector current and compare the results with SPICE. The bias collector current is swept from 0.1 to 1 mA. The measurement uses the circuit in Fig. C.1(a). A DAQ output channel (V_BB) sets the bias currents. Another output channel (V_CC) sets the design bias V_CE at each bias current. The gain of the circuit of Fig. C.1(b) is also measured with particular emphasis on the bias solution and the frequency response.

C.1.1. DC (bias) Formulation

A formulation for obtaining the collector current for a given V_BB [Fig. C.1(a)] is based on the following: From the input loop equation,

Equation C.1

The two relevant transistor characterization equations are (B.6),

and base – emitter dc voltage equation, from (B.7), setting V_BC = 0 for simplicity,

Equation C.2

The equation set above has three unknowns, I_C, I_B, and V_BE. The equations can be combined to obtain a function for I_C,

Equation C.3

A good estimate can be obtained with using V_BE ≈ 0.6 V, giving simply

Equation C.4

The simple expression is sufficient, for example, for selecting a value for R_B in the circuit of Fig. C.1(a) in the BJT amplifier project. We have also neglected the dependence of β_DC on V_BC of (B.11). This is a reasonable approximation for establishing the nominal values for the measurement circuit components.

The collector – emitter voltage, V_CE, is then established with

Equation C.5

In designing a project circuit for a current sweep, R_B and R_C are selected for the highest currents and highest DAQ output voltage. In the amplifier project, the circuit of Fig. C.1(b) uses the resistors from the circuit of Fig. C.1(a). It thus has a unique bias variable and V_CC solution for a given design V_CE requirement. This is based on (C.3) and (C.5) and is

Equation C.6

In the amplifier project, the project Mathcad file is used to find the solution for V_CC [with an educated guess for V_BE, as in (C.4)]. If the result has V_CC > 10 V, the limit from the DAQ, it is necessary to decrease R_C or increase R_B. This may be necessary, as the transistor β_DC is not known with precision at the point of the selection of the resistor values. After measuring the actual V_CC, the result is used in the Mathcad file to compute a value for β_DC from a circuit solution.