本次美国代写主要为电路学相关限时测试

1) Unit 4 Filters (60 pts)
FRIDAY 1.1: Filter Design
Design a bandpass filter with the following specifications. Show your work and justify your calculations.
Include a schematic of your circuit.
a. The passband is 1E4 <ω < 1E6
b. The passband gain should be > 5 db and <10 dB
c. The low frequency stopband rolloff should be 20db/decade
d. The high frequency stopband rolloff shoudl be 60 db/decade
e. The low frequency cutoff frequency, 1E4 [rad/s] should be -3dB relative to the passbnad.
f. The high frequency cutoff frequency, 1E6 [rad/s], should be -3dB relative to the passbnad.
g. You cannot use any first order circuit stages
Build the circuit using BPF LPF
2nd order overdamped circuit
measured across the resistor
R must give ζ > 1
BPF ωcHow 10
4
= ωcLow 10
6
=
3 – corrections 3 – corrections
20
db
dec 20
db
dec
LPF ωc 10
6
double ( ) =
need 0dB correction at 10^6 2nd order underdamped ζ=0.5
40
db
dec
rolloff
pass band gain
10
9
20
2.818 =
20log K ( ) 9db =

K 2.818 =
1
1.818kΩ
1kΩ
+ 





2.818 =
Non inverting amp choose R1 R1 1k = R2 1.818k =
1
R2
R1
+






you know that
denominator must
be
H s ( )
2αs
s
2
2αs + ω0
2
+
= expand and 2α in
numerator can be
given by doing so s 10
4
+( ) s 10
6
+( ) BPF
s
2
1010000 s  + 10000000000 +
H s ( )
1.01 10
6
s 
s 10
4
+( ) s 10
6
+( )
= Now find R/L you can pick R or L
10
3 –
1.01  10
6
 1.01 10
3
 = R 10
3 –
1.01  10
6
 = L 10
3 –
=

R 1.01k =
C 1 10
7 –
 = ω0
2 1
LC
=
1
10
10
1  10
3 –

1 10
7 –
 =
LPF
s 10
6
+( )
2 H s ( )
ω0
2
s
2
2αs + ω0
2
+
= you know that denominator
must be ωc ω0 =
ω0 10
6
=
α 0.5 ω0  = this is the underdamped condition where correction is 0dB
α 5 10
5
 =
pick L 1 10
3 –
 =
ω0
2 1
LC
=
C
1
10
12
1  10
3 –

=
1
10
12
1  10
3 –

1 10
9 –
 =
C 1 10
9 –
 =
2α
R
L
=
2 5  10
5
 1  10
3 –
 1 10
3
 =
R 1k =