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Chapter 13

Q. 13.3

TRANSISTOR OSCILLATOR DESIGN

Design a transistor oscillator at 4 GHz using a GaAs MESFET in a common gate configuration, with a 5 nH inductor in series with the gate to increase the instability. Choose a load network to match to a 50 Ω load, and an appropriate terminating network at the input to the transistor. The scattering parameters of the transistor in a common source configuration are (Z_{0} = 50 Ω) S_{11} = 0.72∠ −116^{◦},S_{12} = 0.03∠57^{◦}, S_{21} = 2.60∠76^{◦}, and S_{22} = 0.73∠ −54^{◦}.

Step-by-Step

Verified Solution

The first step is to convert the common source scattering parameters to the scattering parameters that apply to the transistor in a common gate configuration with a series inductor. (See Figure 13.9a.) This is most easily done using a microwave This is most easily done using a CAD package. The new scattering parameters are

S^{′}_{11} = 2.18 ∠−35^{◦},

S^{′}_{12} = 1.26∠18^{◦},

S^{′}_{21} = 2.75∠96^{◦},

S^{′}_{22 }= 0.52∠155^{◦}.

Note that |S^{′}_{11}| is significantly greater than |S_{11}|, which suggests that the configuration of Figure 13.9a is more unstable than the common source configuration.

Calculating the output stability circle (Γ_{L} plane) parameters from (11.25) gives

C_{L}=\frac{(S^{\prime }_{22}-\Delta^{\prime }S^{\prime *}_{22})^{*}}{\mid S^{\prime }_{22} \mid ^{2}-\mid \Delta^{\prime }\mid ^{2} } =1.08\angle 33^{\circ }

 

R_{L}=\left|\frac{S^{\prime }_{12} S^{\prime }_{21}}{\mid S^{\prime }_{22} \mid ^{2} -\mid \Delta^{\prime }\mid ^{2}} \right| =0.665,

Since\mid S^{′}_{11}\mid = 2.18 > 1, the stable region is inside this circle, as shown in the Smith chart in Figure 13.9b. There is a great amount of freedom in our choice for Γ_{L}, but one objective is to make |Γ_{in}| large. We therefore try several values of Γ_{L} located on the opposite side of the chart from the stability circle, and select Γ_{L}= 0.59∠−104^{◦}. Then we can design a single-stub matching network to convert a 50 Ω load to Z_{L} =20 − j35   Ω, as shown in Figure 13.9a. For the given value of  Γ_{L}, we calculate  Γ_{in} as

\Gamma _{in}=S^{\prime }_{11}+\frac{S^{\prime }_{12} S^{\prime }_{21}\Gamma _{L} }{1-S^{\prime }_{22}\Gamma _{L}}=3.96\angle-2.4^{\circ }

or Z_{in }= −84 − j1.9  Ω. Then, from (13.31), we find Z_{S} as

R_S=\frac{-R_{in}}{3 }               (13.31a)

X_S=-X_{in}                   (13.31b)

Z_{s}=\frac{-R_{in}}{3} -jX_{in}=28 + 1.9   \Omega

Using R_{in}/3 should ensure enough instability for the startup of oscillation. The easiest way to implement the impedance Z_{S} is to use a 90 Ω load with a short length of line, as shown in the figure. It is likely that the steady-state oscillation frequency will differ from 4 GHz because of the nonlinearity of the transistor parameters.

TRANSISTOR OSCILLATOR DESIGN Design a transistor oscillator at 4 GHz using a GaAs MESFET in a common gate configuration, with a 5 nH inductor in series with the gate to increase the instability. Choose a load network to match to a 50 Ω load, and an appropriate terminating network at the input to
TRANSISTOR OSCILLATOR DESIGN Design a transistor oscillator at 4 GHz using a GaAs MESFET in a common gate configuration, with a 5 nH inductor in series with the gate to increase the instability. Choose a load network to match to a 50 Ω load, and an appropriate terminating network at the input to