Attenuator Application Note
Figure 1
This first analysis shows why input and output match are
important in attenuator design. The power level of
in the circuit shown in Figure 1 can be analyzed with the
following equation.
When E = 1 volt,
, and 
are plugged into this equation, the plot of Figure 2 is
generated. E can be 1 volt DC or AC RMS, and
, do not contain reactive components,
or
.
Figure 2, Load Power Plot
The peak of the curve shows that maximum power is transfer to the load when the load and source resistance are equal.
To attenuate the source power while maintaining the
source to load match, an attenuator configuration is necessary where the input
and out match are maintained at all values of attenuation. Since most commonly
available RF/MW attenuators use the 
attenuator configuration and operate from DC to the GHz
range, this application note will analyze the
attenuator configuration shown in Figure 3.
Figure 3,
Attenuator
The following equations are used in
attenuator design.
Where N is the desired loss of the attenuator expressed
as a ratio. N and the attenuation in dB are shown in the following table. When
and N are plugged into the equations shown above, the
resistor values for R1, R2, and R3 of the following table are produced.
|
Attenuator Value(dB) |
N |
|
|
|
|
|
|
3 |
0.50 |
50 |
50 |
292.402 |
292.402 |
17.615 |
|
6 |
0.25 |
50 |
50 |
150.476 |
150.476 |
37.352 |
|
10 |
0.10 |
50 |
50 |
96.248 |
96.248 |
71.151 |
|
20 |
0.01 |
50 |
50 |
61.111 |
61.111 |
247.500 |
Table 1
If a short circuit termination is connected to the output
of the attenuator shown in Figure 2, the input resistance becomes R1 and R3 in
parallel. If no load (open circuit termination) is connected to the output, the
input resistance becomes R1 in parallel with the sum of R2 and R3. Table 2 and
3 give the value of
,
, and Return Loss for an open and short circuit termination.
Reflection
Coefficient = 
Where 
is the source resistance and
is the attenuator input with
connected.
The Return Loss is the ratio of reflected power to input power
Return Loss (dB) =
-20 LOG
|
Attenuator Value (dB) |
|
|
|
Return Loss (dB) |
|
3 |
16.614 |
-0.501 |
0.2510 |
6.0 |
|
6 |
29.924 |
-0.251 |
0.0630 |
12.0 |
|
10 |
40.909 |
-0.100 |
0.0100 |
20.0 |
|
20 |
49.010 |
-0.010 |
0.0001 |
40.0 |
Table 2, Short Circuit Termination
|
Attenuator Value (dB) |
|
|
|
Return Loss (dB) |
|
3 |
150.476 |
0.501 |
0.2510 |
6.0 |
|
6 |
83.545 |
0.251 |
0.0630 |
12.0 |
|
10 |
61.111 |
0.100 |
0.0100 |
20.0 |
|
20 |
51.010 |
0.010 |
0.0001 |
40.0 |
Table 3, Open Circuit (un-terminated)
The proceeding analysis shows that the input return loss of an attenuator terminated with an open or short is always 2 times the attenuator value. In the GHz range, power transfer through an attenuator can be analyzed in the following way. Power connected to an X dB attenuator would travel through the attenuator, undergo X dB attenuation, reflect off the short or open circuit termination, and undergo another X dB attenuation as it travels back to the source.
In the GHz range, leaving the load end of an attenuator un-terminated to simulate an open circuit termination will lead to measurement errors since a small amount of power will radiate from the center pin of the coaxial connector. To achieve reliable GHz test results a shielded open circuit termination is required.
The pertinent numbers of Tables 2 and 3 have been plotted on a condensed version of a Smith Chart shown in Figure 4 to confirm the proceeding analysis.
Figure 4, Condensed Version Smith Chart
