ELEC 477L
Topics in Wireless System Design Lab
Spring 2007
Lab #1: Pi and T Network Attenuators
Introduction
In wireless system tests it is often necessary to reduce the strength of a signal being delivered
from one device to another. For example, testing RF transmitters can involve power levels of
several Watts or even hundreds or thousands of Watts, which is more power than most pieces of
test equipment can absorb without damage. A simple circuit called an attenuator can be used to
reduce the signal level by a specific number of decibels. An attenuator is essentially a modified
voltage divider that not only reduces an input voltage to a lower value but also preserves the
value of load resistance seen by the source. One way to accomplish this is to use a “” or “T”
shaped arrangement of resistors, thus forming a circuit called a pi or T network attenuator. In this
lab exercise, you will design, construct, and test one of these two types of attenuators.
Theoretical Background
Most signal generators and other devices that produce electronic signals are designed to be
connected to loads that have specific impedances (usually real). For example, many wireless
communications devices have input impedances of 50 . Attenuation of a signal can be achieved
simply by adding a resistor in series with the load, as shown in Figure 1. The effect of Rnew is to
reduce the voltage applied to the device, but it also causes the equivalent load resistance Req
“seen” by the source to increase by the amount of the added resistance. The resulting impedance
mismatch is often an undesirable result.
Rnew
+
+
vin
50 
−
vout
−
Req = 50  + Rnew
Figure 1. Simple voltage divider used to reduce the voltage vout applied to the
input of an electronic device.
The voltage applied to the load can be reduced without changing the equivalent load resistance if
the circuit shown in Figure 2 is used instead. The two additional resistors provide an extra degree
of freedom so that, in addition to reducing the voltage by a specified amount, the circuit also
maintains an equivalent load resistance Req of 50  or any other desired value. The term
attenuator is generally reserved for circuits that exhibit attenuation with a controlled input
impedance. Note that the circuit is symmetric; it does not matter which side serves as the input
port and which side serves as the output port. This is an important feature if the attenuator is to
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be located between two devices that send and receive signals to and from one another. Because
the three resistors form a letter T, this topology is known as a T network.
R1
R1
+
+
vin
RL
50 
R2
−
vout
−
Req = 50 
Figure 2. A T network resistive attenuator designed for a 50- system
impedance. The two resistors labeled R1 have the same value.
An alternative topology is shown in Figure 3. This variant is called a pi network attenuator
because the three resistors form the shape of the Greek letter pi. Like the T network, the pi
network has two degrees of freedom (resistor values R1 and R2), so it can be designed for any
desired level of attenuation while simultaneously maintaining a specific load impedance.
R2
R1
R1
RL
50 
Req = 50 
Figure 3. A pi network attenuator designed for a 50- system impedance.
The design equations for the T network attenuator, which give the required values for R1 and R2,
can be found easily using basic circuit analysis techniques. Using the quantities defined in
Figure 2, the equations are
2r
1 r 
R1  RL 
,
 and R2  RL
1 r2
1 r 
where RL is the original load impedance, and r = vout/vin. For example, if the voltage is to be
reduced by a factor of ten in a 50- system, then r = 0.1 and RL = 50 . The pi network design
equations are
1 r2
1 r 
R1  RL 
.
 and R2  RL
2r
1 r 
Note the symmetry between the two sets of equations. The pi and T network topologies are
examples of dual networks; that is, one network is the complement, or dual, of the other.
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Experimental Procedure
The notes and data you take during the following procedures should be organized into an almostprofessional report. A handwritten report is acceptable, as is a word-processed report with
handwritten equations. However, your report should be neat and well organized. Imagine you
are putting together a memo for a manager who is interested in your results but who has not read
this hand-out. Thus, you should include a brief (maybe only one or two sentences) introduction
and a brief conclusion. Only one report is required from each group, and it is due at noon the
day after the lab session. Grades will be quantized by 5 points on a 100-point scale.

Your group will be given specifications for the following attenuator characteristics:
o Topology (Pi or T network)
o Attenuation in dB
o System impedance (50 )
Design an attenuator (i.e., find the resistor values) to meet these specifications. Briefly but
clearly outline your design procedure in your report. Use the closest standard value for each
resistor in the attenuator. Do not combine multiple resistors in series or parallel to form the
required values. Make sure you apply the correct formula for dB loss to find r.

Construct the attenuator you have just designed on a breadboard, and use test cables with
BNC connectors at one end and alligator clips at the other end to provide input and output
connections for the circuit.

For the following measurements you will be using the Agilent E4438C RF signal generator
and the Hewlett-Packard spectrum analyzer. Since Bucknell has only one of each unit, you
will need to take turns with the other lab groups. Set the signal generator to supply an
unmodulated carrier at an output level of around −20 dBm at a frequency of 100 kHz. Use
the spectrum analyzer to confirm that the output level is correct (or to check the analyzer’s
calibration).

Connect your attenuator between the signal generator and the spectrum analyzer. The output
impedance of the generator and the input impedance of the spectrum analyzer are each 50 ,
so they will provide proper terminations for the attenuator circuit. Measure and record the
actual attenuation in dB obtained with your circuit at 100 kHz.

Repeat the attenuation measurements at 10 MHz, 100 MHz, 500 MHz, and 1 GHz, and
record your results. Compare the measured attenuation values to the design value, and give a
plausible explanation for any variations from the design value that you observe.

Construct a new version of your attenuator circuit on the PC board provided to you. Measure
and record the attenuation at 100 kHz, 10 MHz, 100 MHz, 500 MHz, and 1 GHz. Comment
on whether the performance of this attenuator is better than the breadboard version and why.

Use circuit analysis to calculate the voltages at the input and output ports of the attenuator
and the amount of power dissipated by each resistor for an input power of 20 dBm. Be
careful! Make sure you understand what the specification of 20 dBm input power actually
means. Which resistor in the attenuator circuit absorbs the most power?
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