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 \[R3/(R1 + R3 )\]
RIN = 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 = RIN (1 − K)
R2 = RIN × K/(1 − K)
R3 = K × RIN
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.