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 . 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 (ohms) (ohms) (ohms) (ohms) (ohms) 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) with = Short Circuit (Reflection Coefficient) 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) with = Open Circuit (Reflection Coefficient) 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