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1 Quiz 2 Solution Name ________________________ Question 1. Consider the PLL shown where 𝐾𝑣= 104and 𝐾𝑜= 1 krads⁄per V. (a)What is the order of the loop? (1 point)1storder (b)What is the time constant of the loop? (1 point)𝜏= 1𝐾𝑣= 100 𝜇s⁄(c)What is the 3-dB bandwidth of the loop in Hz? (1 point)𝑓3𝑑𝐵= 1 2𝜋𝜏= 1.6 kHz⁄(d)If the input frequency changes with a step, what is the rise time of the VCO control voltage assuming the loop stays in lock? (1 point)𝑡𝑟≈2.2𝜏= 220 𝜇𝑠or 𝑡𝑟≈0.35𝐵𝑊 ≈220 𝜇s⁄(e)Write down an expression for the transfer function 𝐻(𝑠) =𝜃𝑜(𝑠)𝜃𝑖(𝑠)⁄. (2 points) 𝐻(𝑠) =104𝑠+ 104(f)Write down an expression for the transfer function 𝐻(𝑠) =𝑉𝑉𝐶𝑂(𝑠)𝜔𝑖(𝑠)⁄(3 points) 𝐻(𝑠) =104𝑠+ 104=1103104𝑠+ 104=10𝑠+ 104(g)Write down the units for the transfer function 𝐻(𝑠) =𝑉𝑉𝐶𝑂(𝑠)𝜔𝑖(𝑠)⁄(1 point) V/(rad/s) or V s
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