The formulas on this page are associated with Tee or Tpad resistive attenuators. These devices can be used to reduce the amplitude of a given signal so that it can then be safely monitored on a diagnostic device (such as an oscilloscope) without damaging the diagnostic.
These attenuator circuits provide a matched impedance Z between the source and the load (in most cases, this is 50 ohms) and the attenuation factor depends upon the proper load impedance being supplied (e.g. a 50 ohm attenuator must be terminated in 50 ohms in order to attenuate the signal to the appropriate degree).
The table below shows the general equations used to determine the attenuator internal resistances and output voltage attenuation. As can be seen from the schematic diagram below, each attenuator consists of two equal series resistances and a different resistance shunted to ground from the node between the two series values, thus forming the "T" circuit.
TPad Series Resistance 
Z is the load impedance (W) K is the attenuation factor (Vout/Vin) 

TPad Shunt Resistance 
All variables defined as above 

Attenuation in decibels (dB) 
All variables defined as above 
The table below shows the R1 and R2 resistor values for common attenuator values for a 50 ohm impedance Tpad attenuator.
Attenuation Factor (K) 
R1 Resistance 
R2 Resistance 
2 
16.7 
66.7 
5 
33.3 
20.8 
10 
40.9 
10.1 
For the physical implementation of these devices, precision resistors are usually selected and care must be taken in the layout to avoid stray reactance which might cause signal reflections.
The circuit schematic for the Tpad attenuator is shown below. In this specific model, the input waveform is a 1 MHz, 1V ac source and the values shown are for a 10X (20 dB), 50 ohm attenuator.
The results of the circuit model are shown below. V(1) is the 1V, 1 MHz, sinusoidal input voltage. The attenuator output voltages, V(RLOAD), is graphed in the second, lower plot. The waveform plot can be clicked on to open up the full size graph in a separate window.
The calculator below can be used to determine the proper internal resistor values for an attenuator of a given configuration (based on attenuation factor and matching impedance). It will also determine the attenuation in dB. Credit for the initial Javascript code used in the calculator is given to Ray Allen who has a number of similar useful calculators on his website, Pulsed Power Portal.
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