Let us assume that a 50 Ω coaxial transmission line cable needs to drive the input of amplifier with an input resistance of 10 kΩ. In order to maximize power transfer from one stage to the next, the output impedance of the driving stage, the transmission line in this case, must match the input

Question

Let us assume that a 50 Ω coaxial transmission line cable needs to drive the input of amplifier with an input resistance of 10 kΩ. In order to maximize power transfer from one stage to the next, the output impedance of the driving stage, the transmission line in this case, must match the input impedance of the receiving stage, the CB amplifying stage. The output impedance of the CB stage must match the input impedance of the circuit downstream. Figure 6.39a shows this downstream circuit simply as [latex]R_{in}[/latex]. Refer to Figure 6.39a to view the circuit set up. Design a common base amplifier configuration that presents an input impedance of 50 Ω to the coax signals. The amplifier output impedance must be 10 kΩ to match the input impedance [latex]R_{in}[/latex] of the stage that need to be driven.

Accepted Answer

From Equations: (6.86) and (6.88) we know that:

[latex]R_{out}=R_C[/latex] (6.86)

[latex]R_{in}=(1/g_m)//R_E=\frac{R_E}{1+g_m R_E}[/latex] (6.88)

Ignoring the Early effect of the BJT, and

[latex]R_{in}=(1/g_m)//R_E=\frac{R_E}{1+g_m R_E}[/latex] (6.94)

We need the CB stage [latex]R_{in}[/latex] to be 50 Ω, and we need an [latex]R_{out}[/latex] = 10 kΩ. Since [latex]R_{out} = R_C[/latex], if we obtain a BJT with a [latex]g_m[/latex] of 1/53 Ω or 0.0188679 S and [latex]R_E[/latex] = 1 kΩ, it yields

[latex]R_{in}=(1/g_m)//R_E=53//1000≈50 Ω[/latex]

And since we are ignoring the Early effect, [latex]r_o[/latex] → ∞, thus [latex]R_{out}[/latex] simple equals [latex]R_C[/latex], hence:

[latex]R_{out}=10 kΩ[/latex]

Finally, the CB amplifier needs to be biased such that a [latex]g_m[/latex] of 0.0188679 S is obtained. Since [latex]g_m = I_C/V_T and V_T[/latex] = 0.026 V at room temperature, then we need a collector biasing current of

[latex]I_C=g_mV_T=0.0188679 imes 0.026=0.49 mA[/latex]

The selection of resistors [latex]R_1 ext{ and } R_2[/latex] are left as an exercise to the reader.

Question 6.14: Let us assume that a 50 Ω coaxial transmission line cable ne...

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