A T-pad attenuator is an unbalanced attenuator network consisting of three non-inductive resistive elements connected together to form a “T” configuration, (hence its name).

Although not as common, this “T” (tee) configuration can also be thought of as a wye “Y” attenuator configuration as well. Unlike the previous L-pad Attenuator, which has a different resistive value looking into the attenuator from either end making it an asymmetrical, the T-pad attenuator is symmetrical in its design.

The formation of the resistive elements into a letter “T” shape means that the T-pad attenuator has the same value of resistance looking from either end. This formation then makes the “T-pad attenuator” a perfectly symmetrical attenuator enabling their input and output terminals to be transposed as shown.

We can see that the T-pad attenuator is symmetrical in its design looking 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 R2 are of the same value but when designed to operate between circuits of unequal impedance these two resistor can be of different values. In this instance the T-pad attenuator is often referred to as a “taper pad attenuator”.

Related Products: Fixed Attenuator | Voltage Variable Attenuators

But before we look at T-pad Attenuators in more detail we first need to understand the use of the “K factor” used in calculating attenuator impedances and which can make the reduction of the maths and our lives a little easier.

## The Attenuators “K” Factor

The “K” factor, also known as the “impedance factor” is commonly used with attenuators to simplify the design process of complex attenuator circuits. This “K” factor or value is the ratio of the voltage, current or power corresponding to a given value of attenuation. The general equation for “K” is given as:

In other words, the voltage ratio, Kv is given as: Vin/Vout = 10dB/20, the current ratio, Ki is given as: Iin/Iout = 10dB/20, and the power ratio, Kp is given as: Pin/Pout = 10dB/10.

So for example, the “K” value for a voltage attenuation of 6dB will be 10 (6/20) = 1.9953, and an attenuation of 18dB will be 10 (18/20) = 7.9433, and so on. But instead of calculating this “K” value every time we want to design a new attenuator circuit, we can produce a “K” factor table for calculating attenuator loss as follows.

### Attenuator Loss Table

 dB Loss 0.5 1 2 3 6 7.5 9 10 K value 1.0593 1.122 1.2589 1.4125 1.9953 2.3714 2.8184 3.1623
 dB Loss 12 18 24 30 36 48 60 100 K value 3.9811 7.9433 15.849 31.623 63.096 251.19 1000 105

and so on, producing an attenuation loss table with as many decibel values as we require for our attenuator design.

## T-pad Attenuator with Equal Impedances

We have said previously, that the T-pad attenuator is a symmetrical attenuator design whose input and output terminals can be transposed with each other. This makes the T-pad attenuator ideal for insertion between two equal impedances ( ZS = ZL ) 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 T-pad’s input and output impedances are designed to perfectly match the load, this value is called the “characteristic impedance” of the symmetrical T-pad network.

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

where: K is the impedance factor from the table above, and Z is the source/load impedance.

A T-pad attenuator is required to reduce the level of an audio signal by 18dB while matching the impedance of the 600Ω network. Calculate the values of the three resistors required.

Then resistors R1 and R2 are equal to 466Ω and resistor R3 is equal to 154Ω, or the nearest preferred values.

Again as before, we can produce standard tables for the values of the series and parallel impedances required to construct a 50Ω, 75Ω or 600Ω symmetrical T-pad attenuator circuit as these values will always be the same regardless of application. The calculated values of resistors, R1, R2 and R3 are given below.

 dB Loss K factor 50Ω Impedance 75Ω Impedance 600Ω Impedance R1, R2 R3 R1, R2 R3 R1, R2 R3 1.0 1.1220 2.9Ω 433.3Ω 4.3Ω 650.0Ω 34.5Ω 5K2Ω 2.0 1.2589 5.7Ω 215.2Ω 8.6Ω 322.9Ω 68.8Ω 2K58Ω 3.0 1.4125 8.5Ω 141.9Ω 12.8Ω 212.9Ω 102.6Ω 1K7Ω 6.0 1.9953 16.6Ω 66.9Ω 24.9Ω 100.4Ω 199.4Ω 803.2Ω 10.0 3.1623 26.0Ω 35.1Ω 39.0Ω 52.7Ω 311.7Ω 421.6Ω 18.0 7.9433 38.8Ω 12.8Ω 58.2Ω 19.2Ω 465.8Ω 153.5Ω 24.0 15.8489 44.1Ω 6.3Ω 66.1Ω 9.5Ω 528.8Ω 76.0Ω 32.0 39.8107 47.5Ω 2.5Ω 71.3Ω 3.8Ω 570.6Ω 30.2Ω

Note, as the amount of attenuation required by the circuit increases the series impedance values for R1 and R2 also increase while the parallel shunt impedance value of R3 decreases. This is characteristic of a symmetrical T-pad attenuator circuit used between equal impedances.

## T-pad Attenuator with Unequal Impedances

As well as using the T-pad attenuator to reduce signal levels in a circuit with equal impedances, we can also use it for impedance matching between unequal impedances ( ZS ≠ ZL ). When used for impedance matching, the T-pad attenuator is called a Taper Pad Attenuator. 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 become.

### Taper Pad Attenuator Equations for Unequal Impedances

where: K is the impedance factor from the table above, and Z1 is the larger of the source/load impedances and Z2 is the smaller of the source/load impedances.

A taper pad attenuator connected to a load impedance of 50Ω is required to reduce the level of an audio signal by 18dB from an impedance source of 75Ω. Calculate the values of the three resistors required.

Then: Z1 = 75Ω (the largest impedance), Z2 = 50Ω (the smallest impedance) and K = 18dB = 7.9433 from the table above.

So resistor R1 is equal to 15.67Ω, resistor R2 is equal to 62Ω and resistor R3 is equal to 36Ω, or the nearest preferred values.

## Balanced-T Attenuator

The balanced T-pad attenuator or Balanced-T Attenuator for short, uses two T-pad attenuator circuits connected together to form a balanced mirror image network as shown below.

### Balanced-T Attenuator Circuit

The balanced-T attenuator is also called an H-pad attenuator because the layout of its resistive elements form the shape of a letter “H” and hence their name, “H-pad attenuators”. The resistive values of the balanced-T circuit are firstly calculated as an unbalanced T-pad configuration the same as before, but this time the values of the series resistive in each leg are halved (divided by two) to provide a mirror image either side of ground. The total calculated resistive value of the center parallel resistor remains at the same value but is divided into two with the center connected to ground producing a balanced circuit.

Using the calculated values above for the unbalanced T-pad attenuator gives, series resistor R1 = R2 = 466Ω ÷ 2 = 233Ω for all four series resistors and the parallel shunt resistor, R3 = 154Ω the same as before and these values can be calculated using the following modified equations for a balanced-T attenuator.

### Balanced-T Attenuator Equations

The T-pad attenuator is a symmetrical attenuator network that can be used in a transmission line circuit that has either equal or unequal impedances. As the T-pad attenuator is symmetrical in its design it can be connected in either direction making it a bi-directional circuit. One of the main characteristics of the T attenuator, is that the shunt arm (parallel) impedance becomes smaller as the attenuation increases. T-pad attenuators that are used as impedance matching circuits are usually called “taper pad attenuators”.

We have seen that T-pad attenuators can be either unbalanced or balanced resistive networks. Fixed value unbalanced T-pad attenuators are the most common and are generally used in radio frequency and TV coaxial cable transmission lines were one side of the line is earthed. Balanced-T attenuators are also called H-pad Attenuators due to their design and construction. H-pad attenuators are mainly used on data transmission lines which use balanced or twisted pair cabling.

In the next tutorial about Attenuators, we will look at another type of T-pad attenuator design called the Bridged-T Attenuator that uses an additional resistive component in the series line.

• V
Vidyasagar Mekkalki

Reading this it might seem like k=Vo/Vi .but it should be specified that k=Vin /Vo

• M
Matt Hall

Yes, you are right, K is the ratio of input voltage to output voltage.

To make this even more confusing, the formulae (voltage & power) for K given above are transposed.
As an example, with K=2 the output voltage will be half the input, which is 10log(0.5)=-3dB (in voltage terms). That translates to an output power of a quarter of the input power or -6dB (in power terms). Either 20log(Vout/Vin) or 10log(Pout/Pin) gives the same.
The formulae for K should thus be:

K = antilog(dB/20) if dB is the power ratio
K = antilog(dB/10) if dB is the voltage (or current) ratio

• K
Keziah Chandra.J

For testing the above circuit,supply voltage should be in which range?

• Wayne Storr

Its a passive network, any supply voltage is generated by the source circuit and dependant on the power rating of the resistive elements.

• c
chandu

Bbc.co McEwen superb information is gotttteeeeddd

• S
Simon

A dB is a dB, there are not different sorts of dB for voltage or power. The correct equation for K appears to be 10^(dB/10).

Dave : the minmum loss to convert 600 ohms to 50 ohms matching both sides will be quite large, so lower attenuation than this requires gain somewhere which is what the negative resistance is telling you.

• Wayne Storr

The decibel is the ratio between two quantities, usually the input to the output. If the quantity is voltage or current related then: dB = 20log(input/output). If the quantity is power then: dB = 10log(Pin/Pout). You can also use 10log if the voltage or current ratio is first squared: 10log(input/output)^2

• S
Simon

Quite so, but the definition for decibel is basically about the power ratios. The voltage version applies only in limited circumstances (derived from the power situation) such as in RF circuits where the source and load impedances are both often 50 ohms. The use of dB for voltage gain for an amplifier (say) having high input impedance and low output impedance driving a non-matched load is only valid to compare similar amplifiers having differing voltage gains, the source and load remaingn constant.
The problem in the article is that two different ‘K’ values are generated from any particular dB value, which is silly.

There is a nice article on Wikipedia on the decibel.

• Wayne Storr

If you are dealing with voltage ratios, there is only one k value. If you are dealing with current ratios, there is only one k value. If you are dealing with power ratios, there is only one k value. Do not read the inaccuracies of Wikipedia.

• D
DAVE

Brilliant, the K factor figured this would save me plugging in random values of resistor to obtain my 3 attenuation levels. How I was wrong… The impedance from my source is 600 ohms and load is 50. R2 turn out to be negative for all attenuation levels below 17, so that’s -17dB.

Can anyone explain what to do when you get negative resistance with large source impedance?

Thanks

• s
suraj

i do not uderstood the above equietion

• o
omer

why we need attenuator pads in any telecom systems

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