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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