30-06-2012, 02:09 PM
Study of T –type and π- type attenuators.
Study of T –type and π- type attenuators..docx (Size: 30.3 KB / Downloads: 46)
theory:
An attenuator is a two-port resistive network and is used to reduce the signal level from a given amount. In a number of applications it is necessary to introduce a specified loss between source and a matched load without altering the impedance relationship. Attenuators may be used for this purpose. Attenuators may symmetrical or asymmetrical and can be either fixed or variable. A fixed attenuator with constant attenuation is called a pad. Variable attenuators are used as volume controls in radio broadcasting sections. Attenuators are also used in laboratory to obtain small value of voltage or current for testing circuits.
The increase or decrease in power due to insertion or substitution of a new element in a network can be conveniently expressed in decibels (dB), or in nippers. Accordingly, the attenuation offered by a network in decibels is:
Attenuation in dB = 10log10(P1/P2),
where, P1=input Power, P2=output power .
For a properly matched network, both terminal pairs are matched to the characteristic resistance, Ro of the attenuator.
Hence, P1/P2 =I12Ro / I22Ro = I12/I22,
where, I1= input current, I2 = output current leaving the port.
Or, P1/P2 = V12/V22,
where, V1=voltage at port 1, V2= voltage at port 2
Hence, attenuation in dB = 20log10(V1/V2) = 20log10(I1/I2) ,
Also, V1/ V2= I1/ I2 = N, then P1/ P2=N2,
And, dB = 20log10N or N= antilog (dB/20)
T-TYPE ATTENUATOR:
An attenuator is to be designed for desired values of characteristic resistance, Ro and attenuation.
The values of the arms of the network can be specified in terms of
characteristic impedance, Zo , and propagation constant, γ, of the network. This network is a symmetrical resistive circuit; hence Zo = Ro and γ = α. The design equations can be obtained by applying Kirchoff’s laws to the network in the above figure:
I1/ I2 = N = (R1+Ro+R2)/R2
The characteristic impedance of the attenuator is Ro= {R1+[R2 (R1+Ro)]/[ R1+Ro+R2]}
Hence, the values of the resistors are:
R1= Ro(N-1)/(N+1), R2 = 2N Ro/(N2-1)
2. Π- TYPE ATTENUATOR: The values of the arms of the network can be specified in terms of characteristic impedance, Zo ,and propagation constant, γ, of the network. This network is a symmetrical resistive circuit; hence Zo=Ro and γ = α.
From the fundamental equations, we have:
R1= Rosinh α, R2 = Rocoth α/2
Propagation constant = eγ = I1/ I2 = N.
Here, γ = α and eα = N,
Therefore, R1= Ro(N2-1)/2N; R2= Ro(N+1)/(N-1)
PROCEDURE:
1. Connect AF signal generator to attenuator network using variable resistance to attenuator network as shown below:
2. Adjust AF generator output for 1Volt p-p.
3. Adjust variable resistance ® such that VBD is one-half of the voltage VAC. Now, disconnect AF generator and measure the value of the variable resistance R with the help of multimeter. This is the input impedance of the network.
4. Connect AF signal generator to attenuator network using variable resistance to attenuator network as shown above.
5. Adjust AF generator output for 1Volt p-p at the output of the network.