In this project you will design two bandpass filters (a Chebyshev and a Butterwo

Question

In this project you will design two bandpass filters (a Chebyshev and a Butterworth lumped element bandpass filter). Design a lumped element Chebyshev or equal-ripple bandpass filter that meets meet the following performance specifications: Center frequency, f_0 = 10 MHz. Bandwidth, B W_f = 1.0 MHz. Ripple = 0.2 dB. IL greaterthanorequalto 30 dB for f = f_q1 = 9 MHz. IL greaterthanorequalto 35 dB for f =f_q2 = 11.5 MHz. The source and load impedances of the filter are 50 - Ohm. For the filter designed in Task (1), plot the gain in dB versus frequency. Employ a frequency range of 8 to 12 MHz and a range of - 60 to 0 dB for the gain. Design a lumped element Butterworth bandpass filter that employs the same order as the filter in Task (1). For the filter designed in Task (3), plot the gain in dB versus frequency. Employ a frequency range of 8 to 12 MHz and a range of - 60 to 0 dB for the gain. On the same graph, plot the gain of the filters designed in Task (1) and Task (3). Employ a frequency range of 8 to 12 MHz and a range of - 60 to 0 dB for the gain.

Explanation / Answer

For example, we might be interested in determining the output impedance of a

120Vrms power outlet. Between the generating station (where V

th

(t) is located) and the

wall outlet there are likely to be miles of

transmission lines, transformers, resistive

losses, stray capacitances, etc. Since it is generally impractical to measure all the

individual impedances between the generat

or and the outlet, we would rather simplify

the network and lump all the effects into a

single

output impedance, Z

out

, that can be

measured directly at the outlet.

*

The ThÈvenin impedance (the output impedance in this case) is defined to be the

complex ratio of the open circuit voltage an

d the short circuit current. In order to

determine the ThÈvenin voltage we simply

measure the open circuit voltage.

However, the short circuit current presents several practical problems in attempting to

determine the ThÈvenin impedance. First, we need the

phase

relationship between the

voltage and current in the circuit, which me

ans the two measurements must be made at

the same time so that the relative phase can be determined. It is not possible to have

both an open circuit and short circuit measur

ement at the same time. Second, even if

we are only interested in the magnitude of th

e impedance and not the phase, it is often

impractical to "short out" the circuit due to

the large current that may flow if the output

impedance is small. For example, in the 120V wall outlet mentioned in the previous

paragraph, applying a short circuit to the

output should cause the fuse or circuit

*

Note tha

t although ma

ny mul

timeters mea

sure resistance, they are designed for use with

passi

ve

circuits

onl

y (a sma

ll vol

tage source i

n the meter i

s used to pa

ss a

current through the components under test)

.

Hooki

ng such a

meter to a

n

active

circuit

(like a wall out

let) in ord

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