0195136047.pdf

PROBLEMS 197

the overall transfer function is given by

TBS(s)=TLP(s)+THP(s)

Using MATLAB, plot the bandstop response.

3.6.7An expression for a sawtooth wave over the in-
ternal 0≤t ≤T 0 is given byf(t)=At/T 0.
The student is encouraged to check the Fourier
coefficients to bea 0 =A/ 2 ,an=0 for alln, and
bn=−A/(nπ )for alln. The Fourier series for
the sawtooth wave is then given by

f(t)=

A

2

+

∑∞

n= 1

(

−

A

nπ

)

sin( 2 πnt/T)

Using MATLAB, withA=10 andT 0 =2 ms,

plot the truncated series representations of the

waveformf( 5 ,t), which is the sum of the dc com-

ponent plus the first 5 harmonics, andf( 10 ,t),

which is the sum of the dc component plus the

first 10 harmonics.

3.6.8The steady-state circuiti(t)in a seriesRLcircuit
due to a periodic sawtooth voltage is given by

i(t)=

VA

2 R

+

VA

R

∑∞

n= 1

1

nπ

√

1 +(nω 0 L/R)^2

cos(nω 0 t+90°−θn)

whereθn=tan−^1 (nω 0 L/R). With the parameters

VA=25 V,T 0 = 5 μs,ω 0 = 2 π/T 0 ,L= 40 μH,

andR= 50 , by using MATLAB, plot truncated

Fourier series representations ofi(t)using the dc

plus first 5 harmonics and the dc plus first 10

harmonics.

Hint:

I 0 =

VA

2 R

; In=

VA

R

1

nπ

√

1 +(nω 0 LR−^1 )^2

;

θn=tan−^1 (nω 0 L/R)

f(k,t)=I 0 +

∑k

m= 1

Imcos(mω 0 t+ 0. 5 π−θm)

Plot fromt=0to2T 0 with a time-step interval

ofT 0 / 400.

+

+

−

−

R 1 = 200 Ω C 2 = 0.1 μF

Vin C 1

__

Vout

__

10 μF R 2 = 2 kΩ

1 23

O

Figure P3.5.11

+

+

−

−

1.59 kΩ

v 1 (t)

C

10 nF

R

L

12 μH v 2 (t)

(a)

+

+

−

−

R

V 1 (s) Ls Cs^1 V 2 (s)

(b)

Figure P3.6.4(a)t-domain.(b)s-domain.

+

+

High-pass filter

ωCHP >> ωCLP

Low-pass filter

ωCLP

Figure P3.6.6Bandstop filter through the parallel connec-

tion of high-pass and low-pass filters.