Consider the shown circuit, where $\backslash (\backslash$mathrm$\{$R$\}=500\backslash$Omega$,\backslash$mathrm$\{$~L$\}=40\backslash$mu $\backslash$mathrm$\{$H$\},\backslash$mathrm$\{$C$\}=30\backslash$mathrm$\{$nF$\}\backslash ),$ and Vs is a sinusoidal source with a peak amplitude of $\backslash (5\backslash$mathrm$\{$~V$\}.(\backslash$quad V s$($t$)=5\backslash$cos $(\backslash$omega t$)\backslash$quad $\backslash$mathrm$\{$V$\})\backslash )$

Part $1$: Hand Calculation

a$)$ Assume the source has a frequency of $140$ kHz $,$ calculate:

$1.$ the impedance Z seen by the source $($expressed as a complex number and as magnitude$/$phase$).$ Is the impedance capacitive or inductive $?$

$2.$ the source current Is$.($Expressed as a Phasor and as a time function$)$

$3.$ the voltage Vo $($Expressed as a Phasor and as a time function$)$

b$)$ Repeat part $($a$)$ at a frequency of $148$ kHz

c$)$ Calculate the resonant frequency of the circuit $($the frequency at which the reactive components cancel each other$)$

d$)$ find the impedance of the circuit at the resonant frequency

e$)$ Calculate the Quality factor and the $3-$dB bandwidth of the circuit. Note that the resonator $($LC circuit$)$ is parallel

Part $2$: Simulation

Draw the circuit on LTSpice

a$)$ Perform AC analysis $($from $130$ kHz to $170$ kHz $,$ use linear scale with $10000$ points$)$ and plot the following on a separate plot:

$-$ The voltage $($Vo$)$

$-$ The current $($Is$)$

$-$ The impedance seen by the source

b$)$ From the plots verify your results in the hand calculation for parts $($a$)$ and $($b$)$

c$)$ from the plots find the resonant frequency

d$)$ From the voltage plot, find the $3-$dB bandwidth.