Question $2.$ A first$-$order PLL with $K_y={10}^4{s}^{-1}$ uses a VCO with $K_a=2kH\frac{z}{V}$ and free running frequency of $10$ kHz when $v_e=0V.$ Assume the PLL is initially locked to a $20-$ kHz signal. At $i=0,$ the input signal changes to $16$ kHz $.$ Find the equation for the VCO control voltage $v_z(c)$ and sketch its response vs$,$ time, $(10$ points$)$

Question $3.$ Referring to the PLL describsd in Question $2,$ if the VCO sensitivity is increased by a factor of $2,$ the time for $v_e(t)$ to sette to within $1\%$ of it's final value after a step change in the input frequency will be $($choose the hest answer$)(5$ Points$)$

a$)$ Slower than the original PLL

b$)$ Faster than the original PLL

c$)$ The same as the original PLL