As well as T-pad attenuators, there is another type of voltage controlled attenuator design commonly used in radio frequency and microwave transmission lines called the **Pi-pad Attenuator**, or **π-pad attenuator**.

The *Pi-pad attenuator* is so called because its design resembles that of the Greek letter pi ( π ) meaning that it has one series resistor and two parallel shunt resistors to ground at the input and the output.

The Pi-pad attenuator is another fully symmetrical purely resistive network that can be used as a fixed attenuator between equal impedances or for impedance matching between unequal impedances. The circuit configuration of the Pi-pad attenuator is given below.

We can see that the standard pi-pad attenuator is symmetrical looking at the attenuator from either end and this type of attenuator design can be used to impedance match either equal or unequal transmission lines. Generally, resistors R1 and R3 are of the same value but when designed to operate between circuits of unequal impedance these two resistor can be of different values.

We have said previously, that the pi pad attenuator is a symmetrical attenuator design consisting solely of passive resistor elements making it linear in its design allowing for its input and output terminals to be transposed with each other. This makes the pi pad attenuator ideal for insertion between two equal impedances ( Z_{S} = Z_{L} ) to reduce signal levels.

In this case the three resistive elements are chosen to ensure that the input impedance and output impedance match the load impedance which forms part of the attenuator network. As the Pi-pad’s input and output impedances are designed to perfectly match the load, this value is called the “characteristic impedance” of the symmetrical Pi-pad network.

Then the equations given to calculated the resistor values of a Pi-pad attenuator circuit used for impedance matching at any desired attenuation are given as:

where: K is the impedance factor and Z is the source/load impedance.

A Pi-pad attenuator circuit is required to reduce the level of an audio signal by 10dB while matching the impedance of a 75Ω network. Calculate the values of the three resistors required.

Using our simple table of “K factors”, we can see that the “K” factor value for calculating attenuation loss of -10dB is given as **3.1623**.

dB | 0.5 | 1.0 | 2.0 | 3.0 | 4.0 | 5.0 | 6.0 | 10.0 | 20.0 |

“K” value | 1.0593 | 1.1220 | 1.2589 | 1.4125 | 1.5849 | 1.7783 | 1.9953 | 3.1623 | 10.000 |

Then resistors R1 and R3 are equal to 144Ω and resistor R2 is equal to 107Ω, or the nearest preferred values.

Also note that the same pi-pad attenuator design will have different resistor values for one used on a 75Ω network than for one that is being matched to a 50Ω or 600Ω network.

Again as with the T-pad Attenuator, we can produce standard tables for the values of the series and parallel impedances required to construct a 50Ω, 75Ω or 600Ω symmetrical Pi-pad attenuator circuit. The calculated values of resistors, R1, R2 and R3 are given as.

dB Loss | K factor | 50Ω Impedance | 75Ω Impedance | 600Ω Impedance | |||

R1, R3 | R2 | R1, R3 | R2 | R1, R3 | R2 | ||

1.0 | 1.1220 | 869.5Ω | 5.8Ω | 1K3Ω | 8.7Ω | 10K4Ω | 69.2Ω |

2.0 | 1.2589 | 436.2Ω | 11.6Ω | 654.3Ω | 17.4Ω | 5K2Ω | 139.4Ω |

3.0 | 1.4125 | 292.4Ω | 17.6Ω | 438.6Ω | 26.4Ω | 3K5Ω | 211.4Ω |

6.0 | 1.9953 | 150.5Ω | 37.4Ω | 225.7Ω | 56.0Ω | 1K8Ω | 448.2Ω |

10.0 | 3.1623 | 96.2Ω | 71.2Ω | 144.4Ω | 106.7Ω | 1K2Ω | 853.8Ω |

18.0 | 7.9433 | 64.4Ω | 195.4Ω | 96.6Ω | 293.2Ω | 772.8Ω | 2K3Ω |

24.0 | 15.8489 | 56.7Ω | 394.6Ω | 85.1Ω | 592.0Ω | 680.8Ω | 4K7Ω |

32.0 | 39.8107 | 52.6Ω | 994.6Ω | 78.9Ω | 1K5Ω | 630.9Ω | 11K9Ω |

Note, that as the amount of attenuation loss required by the Pi-pad circuit increases, the impedance of the series resistor R2 also increases while at the same time, the parallel shunt impedance values of both resistors R1 and R3 decrease.

This is a common characteristic of a symmetrical Pi-pad attenuator circuit used between equal impedances. Also, even at an attenuation of 32dB the series impedance values are still fairly high and not in the one or two ohm range as with the T-pad attenuator.

This means then that a single **Pi-pad attenuator** network can achieve much higher levels of attenuation compared to the equivalent T-pad network as the parallel shunt impedances are never less than the characteristic impedance of the transmission line due to the extremely high “K” factor value. For example, a transmission line with a characteristic impedance of 50Ω with an attenuation of -80dB would give shunt resistors R1 and R3 a value of 50Ω each while the series resistor R2 would be equal to 250KΩ,

As well as using the Pi-pad attenuator to reduce signal levels in a circuit with equal impedances, ( Z_{S} = Z_{L} ) we can also use it for impedance matching of unequal source and load impedances ( Z_{S} ≠ Z_{L} ). However, to do so we need to modify the previous equations a little to take into account the unequal loading of the source and load impedances on the attenuator circuit. The new equations given for calculating the resistive elements of a Pi-pad attenuator for unequal impedances are.

where: K is the impedance factor, Z_{S} is the larger of the source impedance and Z_{L} is the smaller of the load impedances.

We can see that the equations for calculating the Pi attenuators three resistor values are much more complex when it is connected between unequal impedances due to their effect on the resistive network. However, with careful calculation we can find the value of the three resistances for any given network impedance and attenuation as follows:

An unbalanced non-symmetrical **Pi-pad attenuator** circuit is required to attenuate a signal between a radio transmitter with an output impedance of 75Ω and a power signal strength meter of impedance 50Ω by 6dB. Calculate the values of the required resistors.

Giving us the following non-symmetrical Pi attenuator circuit:

The maths involved for calculating the resistor values of a Pi-pad attenuator used between unequal impedances is more complex than those used to calculate the values between equal impedances. As such Pi-pad attenuators tend to be used more for signal attenuation on transmission lines with matching source/load impedances Z_{S} = Z_{L} .

The **balanced-Pi attenuator** or “Balanced-π Attenuator” for short, uses an additional resistive element in the common ground line to form a balanced resistive network as shown below.

The balanced-Pi attenuator is also called an **O-pad attenuator** because the layout of its resistive elements form the shape of a letter “O” and hence their name, “O-pad attenuators”. The resistive values of the balanced-Pi circuit are firstly calculated as an unbalanced Pi-pad configuration connected between equal impedances the same as before, but this time the value of the series resistor R2 is halved (divided by two) placing half in each line as shown. The calculated resistive value of the two parallel shunt resistors remain at the same.

Using the values previously calculated above for the unbalanced Pi-pad attenuator gives, series resistor R2 = 106.7÷2 = 53.4Ω for the two series resistors and the parallel shunt resistors, R1, R3 = 144.4Ω the same as before.

**Pi-pad Attenuators** are one of the most commonly used symmetrical attenuator circuit and as such its design is used in many commercially available attenuator pads. While the Pi-pad attenuator can achieve a very high level of attenuation in one single stage, it is better to build a high loss attenuator over 30dB by cascading together several individual Pi-pad sections so that the final level of attenuation is achieved in stages.

By cascading together pi-pad attenuators, the number of resistive elements required in the design can be reduced as adjoining resistors can be combined together. So for the Pi-pad this simply means that the two adjoining parallel shunt resistors can be added together.

The accuracy of the calculated pi attenuator will determined by the accuracy of the component resistors used. Which ever tolerance of resistor is selected to construct a **Pi attenuator** circuit, 1%, 5% or even 10% they MUST all be non-inductive resistors and not wirewound types. Also as we are using resistors in the attenuation network these non-inductive resistors MUST be able to safely dissipate the required amount of electrical power as calculated using Ohms Law.

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I would appreciate it if you could post somewhere the formulas that solve for ‘K’.

This is a great article, but it only does half the job…

Using these formulae, I can determine what resistor values I should have. However, even using multiple E24 standard resistors, I can’t match these values exactly in real life.

Given a set of real resistor values, how do I calculate the ACTUAL attenuation? Input and output impedance?

Hello Alan, if you have the resistor values already, just reverse engineer the formulas to make “k” the subject to find the actual attenuation.

Thank, with the help of this site (and a few others) I did just that. Pi and Tee all on a single page. Would you like a (PDF) copy?

Hello Alan, I am happy you were able to solve your problem. ðŸ™‚

You can send a copy to my email address if you so wish.