THEME: RF circuit representations

Problem $1$: ABCD parameter matrix

Figure $1$ shows the circuit with series impedance $Z$ and shunt admittance $Y.$ If the series

impedance $Z$ comprises a $1k$ resistor in series with a $1$ mH inductor and the shunt

admittance $Y$ comprises a $1$ mS resistor in parallel with a $1F$ capacitor, find the $[$ABCD$]$

parameter matrix of this circuit.

Problem $2$: ABCD parameter matrix

Find the ABCD parameter matrix for a lossless transmission line of length $lm$ and

characteristic impedance $Z_0$ as shown in Figure $2.$ Then, calculate the values of the

parameters of the ABCD matrix for $l=\frac{}{4}$ and $Z=100.$

Figure $2$: Lossless transmission line

Problem $3$: $S$ parameter matrix for series impedance

Find the $[$S$]$ parameter matrix for the series impedance $Z=3+j4k$ shown in Figure $3.$

Use the system reference load impedance of $Z_n=50$ in the calculation.

Problem $4$: $S$ parameter matrix for resistive circuit

Find the $S$ parameter matrix for the two$-$port resistive network shown in Figure $4.$ Use

the system reference load impedance of $Z_0=50$ in the calculation.

$[$ABCD$]$ parameter matrix of the network.

$[S]=\left[\begin{array}{cc}-0\mathrm{.}2& 0\mathrm{.}4\\ 0\mathrm{.}4& -0\mathrm{.}3\end{array}\right]$

THEME: RF Oscillator Design

RF transistor oscillator:

Design the transistor oscillator at $10$ GHz using the GaAs FET in a common$-$gate $($CG$)$ configuration with $[$S$]$ parameter matrix at $10$ GHz as follows:

$[S]=\left[\begin{array}{cc}\frac{2\mathrm{.}18}{{?}_{-}}35& \frac{1\mathrm{.}26}{{?}_{18}}\\ \frac{2\mathrm{.}75}{{?}_{96}}& \frac{0\mathrm{.}52}{{?}_{155}}\end{array}\right]$

An inductor $L_G=5nH$ is placed in series with the gate $(G)$ to increase positive feedback and sustain the unstable, oscillatory behavior.

Deliverable:

Word$-$formatted report, submitted to Blackboard, with the following evidence.

$($a$)$ Design steps of the complete circuit

$($b$)$ Complete circuit diagram with labels

Optional submission:

$($c$)$ Altium$/$Pspice diagram of the simulated oscillator circuit, and

$($d$)$ Test and evaluation $($in Altium$/$Pspice$)$ of the oscillator circuit.

THEME: RF Oscillator Design

RF transistor oscillator:

Design the transistor oscillator at $10$ GHz using the GaAs FET in a common$-$gate $($CG$)$ configuration with $[$S$]$ parameter matrix at $10$ GHz as follows:

$[S]=\left[\begin{array}{cc}\frac{2\mathrm{.}18}{{?}_{-}}35& \frac{1\mathrm{.}26}{{?}_{18}}\\ \frac{2\mathrm{.}75}{{?}_{96}}& \frac{0\mathrm{.}52}{{?}_{155}}\end{array}\right]$

An inductor $L_G=5nH$ is placed in series with the gate $($G$)$ to increase positive feedback and sustain the unstable, oscillatory behavior.

Deliverable:

Word$-$formatted report, submitted to Blackboh$-$d$,$ with the following evidence.

$($a$)$ Design steps of the complete circuit

$($b$)$ Complete circuit diagram with labels

Optional submission:

$($c$)$ Altium$/$Pspice diagram of the simulated oscillator circuit, and

$($d$)$ Test and evaluation $($in Altium$/$Pspice$)$ of the oscillator circuit. Solve this question in detail, step by step,but make sure it is $100\%$ correct