# Pi type Attenuator / Pi-pad Attenuator

The pi-pad debilitator is called in this way because of its basic layout and design similar to the letter pi ( π); this means that there is a series of resistance to the soil and two parallel shunt resistances at the entrance and exit.

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Pi-pad debilitating is another completely symmetrically fully resistant network that can be used as a constant attenuator between equal impedances or for impedance matching between unequal impedances. The circuit configuration of the pi-pad debilitator is given below.

We can see that the standard pi-pad debilitator is symmetrical when viewed from both ends of the debilitating, and this type of debilitating design can be used for impedance matching of even or unequal transmission lines. In general, the R1 and R3 resistors are of the same value, but when they are designed to work between unequal impedance circuits, these two resistors can be of different values.

## Equal Impedance Pi-pad Debilitating

We have previously said that the pi pad debilitator has a symmetrical debilitating design consisting only of passive resistance elements, which allows the input and output terminals to be linear in its design, which allows them to be replaced by each other. This makes it ideal to place the pi pad debilitator between two equal impedances (ZS = ZL) to reduce signal levels.

In this case, three resistant elements are selected to ensure that the input impedance and output impedance match the load impedance that forms part of the debilitating network. Since the pi-pad's input and output impedances are designed to fit the load perfectly, this value is called the "characteristic impedance" of the symmetrical Pi-pad network.

The equations given to calculate the resistance values of a Pi-pad debilitating circuit, which is then used for impedance compatibility in any desired weakening, are used as follows:

K is the impedance factor and Z is the welding/load impedance.

## Pi-pad Debilitating Sample

A Pi-pad debilitating circuit is required to reduce the volume of a sound signal by 10dB when pairing the 75Ω impedance. Calculate the values of the three required resistances.

Using our simple "K factors" table, we can see that the factor value "K" is given as 3.1623 to calculate the weight loss of -10dB.

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

Also note that the same pi-pad debilitating design will have different resistance values than those used in the 75Ω network that match the 50Ω or 600Ω network.

Again, as with the T-pad Debilitator, we can produce standard tables for the serial and parallel impedance values required to create a 50Ω, 75Ω or 600Ω symmetrical Pi-pad debilitating circuit. The calculated values of the resistors are given as R1, R2 and R3.

## Pi-pad Debilitating Resistance Values

dB Loss | K value | 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 weight loss required by the pi-pad circuit increases, the impedance of serial resistance R2 increases, and at the same time the parallel shunt impedance values of both R1 and R3 resistors decrease.

This is a common feature of a symmetrical Pi-pad debilitating circuit used between equal impedances. Also, even at a weakening of 32dB, the serial impedance values are still quite high and not in the range of one or two ohms, as with the T-pad debilitator.

This means that a single Network of Pi-pad debilitators can achieve much higher levels of weakening compared to the equivalent T-pad network, since parallel shunt impedances are never less than the characteristic impedance of the transmission line due to extremely high "K". factor value. For example, a transmission line with a 50Ω characteristic impedance with a weakening of -80dB will value each of the R1 and R3 shunt resistors at 50Ω, while the serial resistance will be equal to R2 250KΩ,

## Unequal Impedance Pi-pad Debilitating

In addition to using Pi-pad debilitator to reduce signal levels in a circuit with equal impedances (ZS = ZL), we can also use this type of debilitator for impedance matching of unequal welding and load impedances (ZS ≠ ZL).

However, to do this, we need to slightly change the previous equations to take into account the unequal loading of resource and load impedances on the debilitating circuit. New equations for calculating the resistant elements of a Pi-pad debilitator for unequal impedances.

### Pi-pad Debilitating Equations for Unequal Impedances

K is the impedance factor, ZS is the large one of the welding impedance, and ZL is the smallest of the load impedances.

We can see that the equations for calculating the three resistance values of pi debilitators are much more complex when connected between unequal impedances due to their effects on the resistant network. However, with careful calculation, we can find the value of three resistances for any given network impedance and weakening as follows:

### Pi-pad Debilitating Sample

An unstable, non-symmetrical Pi-pad debilitating circuit is required to weaken a signal between a radio transmitter with a 75Ω output impedance and a 50Ω impedance power signal power meter with 6dB. Calculate the values of the necessary resistors.

Resistance R1 Value

Resistance R2 Value

Resistance R3 Value

After all:

The mathematics used to calculate the resistance values of a Pi-pad debilitator used between unequal impedances is more complex than those used to calculate values between equal impedances. Such Pi-pad debilitators tend to be used more for signal weakening in transmission lines whose matching weld/load impedances are ZS = ZL.

## Balanced Pi-type Debilitating

Balanced-Pi attenuator, or "Balanced-π Attenuator" for short, uses an additional resistance element in the common soil line to form a balanced resistant network, as shown below.

The Balanced-Pi debilitator is also called O-pad debilitating, since the placement of its resistant elements creates the shape of an "O" letter, and therefore its names are "O-pad debilitators". The resistance values of the Balanced-Pi circuit are first calculated as an unbalanced Pi-pad configuration that connects between the same equal impedances as the previous one, but this time the value of the serial resistance R2 is halved (divided in half), placing it in half on each line. The calculated resistance value of the two parallel shunt resistors remains the same.

Using previously calculated values for the unstable Pi-pad debilitator, the serial resistance for two series of resistances and parallel shunt resistors is the same as the previous one R2 = 106.7÷2 = 53.4Ω, R1, R3 = 144.4Ω.

Pi-pad Attenuators are one of the most widely used symmetrical debilitating circuits and therefore their design is used in many debilitating circuits available on the market. While pi-pad can achieve a very high level of weakening in a single debilitating stage, it is better to gradually combine several separate Pi-pad sections to create a high-loss debilitator above 30dB, so that the final weight loss level is achieved in stages.

By gradually connecting pi-pad debilitators together, the number of resistance elements required in the design can be reduced, as adjacent resistors can be combined. For pi-pad, this simply means that two adjacent parallel shunt resistances can be added together.

The accuracy of the calculated pi attenuator is determined by the accuracy of the component resistors used. Regardless of which resistance tolerance is selected to create a Pi debilitating circuit, all 1%, 5% and even 10% must be non-inductive resistors and not wired types. In addition, since we use resistors in the slimming network, these non-inductive resistors should be able to safely distribute the necessary amount of electrical power, as calculated using the Ohm Act.