The R-2R ladder, a well known resistor topology, is often used to implement a current or voltage 6-dB step attenuator. By appropriately scaling the resistor values, this network also can be modified to provide any desired attenuation.

The modified resistor ladder uses three different resistor values *(see the figure)*. A short algebraic manipulation can show that:

Step attenuation (dB) = 20 log \[R3/(R1 + R3 )\]

R_{IN} = R1 + R3

R2 = R3 (1 + R3/R1)

If R1 = R3, then R2 = 2 × R1. In this case, the R-2R network provides a 6-dB step attenuation.

To determine the resistor values for a specific step attenuation and input resistance, use the formulas:

K = 10^{\[step attenuation (dB)/20\]}

(Note that the step attenuation (dB) value should be negative!)

R1 = R_{IN} (1 − K)

R2 = R_{IN }× K/(1 − K)

R3 = K × R_{IN}

For example, to implement a resistor ladder with a −1.5-dB step attenuation and 500-Ω input impedance:

K = 0.8414

R1 = 500 (1 − 0.8414) = 79.3 Ω

R2 = 500 × 0.8414/(1 − 0.8414) = 2653 Ω

R3 = 0.8414 × 500 = 420.7 Ω

There are a couple of interesting points to observe about the PGA circuit. A standard CMOS analog switch is used to connect the attenuated signal to the noninverting input of the op amp, which has a high input impedance. Since the current through the switch is negligible, low attenuation and distortion is achieved. A wide-bandwidth (video-bandwidth), low-distortion PGA is created through the use of very low-cost standard devices.