Quiz02Solution - Quiz 2 Solution Name Question 1 Consider...

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1 Quiz 2 Solution Name ________________________ Question 1. Consider the PLL shown where 𝐾 𝑣 = 10 4 and 𝐾 𝑜 = 1 krad s per V . (a) What is the order of the loop? (1 point) 1 st order (b) What is the time constant of the loop? (1 point) 𝜏 = 1 𝐾 𝑣 = 100 𝜇 s (c) What is the 3-dB bandwidth of the loop in Hz? (1 point) 𝑓 3𝑑𝐵 = 1 2 𝜋𝜏 = 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) 𝑡 𝑟 2.2 𝜏 = 220 𝜇𝑠 or 𝑡 𝑟 0.35 𝐵𝑊 ≈ 220 𝜇 s (e) Write down an expression for the transfer function 𝐻 ( 𝑠 ) = 𝜃 𝑜 ( 𝑠 ) 𝜃 𝑖 ( 𝑠 ) . ( 2 points ) 𝐻 ( 𝑠 ) = 10 4 𝑠 + 10 4 (f) Write down an expression for the transfer function 𝐻 ( 𝑠 ) = 𝑉 𝑉𝐶𝑂 ( 𝑠 ) 𝜔 𝑖 ( 𝑠 ) ( 3 points ) 𝐻 ( 𝑠 ) = 10 4 𝑠 + 10 4 = 1 10 3 10 4 𝑠 + 10 4 = 10 𝑠 + 10 4 (g) Write down the units for the transfer function 𝐻 ( 𝑠 ) = 𝑉 𝑉𝐶𝑂 ( 𝑠 ) 𝜔 𝑖 ( 𝑠 ) ( 1 point ) V/(rad/s) or V s
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