Graphics UnitMath Example: ( Attenuators )
Last Modified: 1/21/2000

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The following examples show how to use UnitMath electrical attenuators.

I have tried to make sure the following formulas are correct, but I do not guarantee them.


T Attenuator TOP

The following figure shows a T attenuator.

Graphics

Given Z1 & Z2 ( Z1 >= Z2 ) R1, R2, & R3 can be found using the following equations. .

MinimumLossIndB: 10 log( ( sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ) )^2 );

R3: 2 sqrt( N Z1 Z2 ) / ( N - 1 );
R1: Z1 ( N + 1 ) / ( N - 1 ) - R3;
R2: Z2 ( N + 1 ) / ( N - 1 ) - R3;

Where N is the desired loss of the attenuator.

Following are example calculations for a T attenuator.

Z1: 273 ohm;
Z2: 50 ohm;
MinimumLoss: (sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ))^2; ~ 19.79
MinimumLossInDb: 10 log( MinimumLoss ); ~ 12.96

lossInDb: 13;
N:10^( lossInDb / 10) ~ 19.95
R3: 2 sqrt( N Z1 Z2 ) / ( N - 1 ); ~ 55.07 ohm
R1: Z1 ( N + 1 ) / ( N - 1 ) - R3; ~ 246.74 ohm
R2: Z2 ( N + 1 ) / ( N - 1 ) - R3 ~ 0.20 ohm


Z1: 75 ohm;
Z2: 50 ohm;
MinimumLoss: (sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ))^2; ~ 3.73
MinimumLossInDb: 10 log( MinimumLoss ); ~ 5.72

lossInDb: 6;
N:10^( lossInDb / 10) ~ 3.98
R3: 2 sqrt( N Z1 Z2 ) / ( N - 1 ); ~ 81.97 ohm
R1: Z1 ( N + 1 ) / ( N - 1 ) - R3; ~ 43.34 ohm
R2: Z2 ( N + 1 ) / ( N - 1 ) - R3 ~ 1.57 ohm


Pi Attenuator TOP

The following figure shows a pi attenuator.

Graphics

Given Z1 & Z2 ( Z1 >= Z2 ) R1, R2, & R3 can be found using the following equations.

MinimumLossIndB: 10 log( ( sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ) )^2 );

R3: 1/2 ( N - 1 ) sqrt( Z1 Z2 / N );
R1: 1/( 1/Z1 ( N + 1 ) / ( N - 1 ) - 1/R3 );
R2: 1/(1/Z2 ( N + 1 ) / ( N - 1 ) - 1/R3 );

Where N is the desired loss of the attenuator.

Following are example calculations for a pi attenuator.

Z1: 75 ohm;
Z2: 50 ohm;
MinimumLoss: (sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ))^2; ~ 3.73
MinimumLossInDb: 10 log( MinimumLoss ); ~ 5.72

lossInDb: 6;
N:10^( lossInDb / 10) ~ 3.98
R3: 1/2 ( N - 1 ) sqrt( Z1 Z2 / N ); ~ 45.75 ohm
R1: 1/( 1/Z1 ( N + 1 ) / ( N - 1 ) - 1/R3 ); ~ 2,386.20 ohm
R2: 1/(1/Z2 ( N + 1 ) / ( N - 1 ) - 1/R3 ) ~ 86.52 ohm


Z1: 273 ohm;
Z2: 50 ohm;
MinimumLoss: (sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ))^2; ~ 19.79
MinimumLossInDb: 10 log( MinimumLoss ); ~ 12.96

lossInDb: 15;
N:10^( lossInDb / 10) ~ 31.62
R3: 1/2 ( N - 1 ) sqrt( Z1 Z2 / N ); ~ 318.11 ohm
R1: 1/( 1/Z1 ( N + 1 ) / ( N - 1 ) - 1/R3 ); ~ 1,318.05 ohm
R2: 1/(1/Z2 ( N + 1 ) / ( N - 1 ) - 1/R3 ) ~ 55.06 ohm


Minimum-Loss Pad TOP

The following figure shows a Minimum-Loss Pad.

Graphics

Given Z1 & Z2 ( Z1 > Z2 ) R1 & R2 can be found using the following equations.

LossIndB: 20 log( sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ) );

R1: Z1 sqrt( 1 - Z2 / Z1 );
R2: Z2 / sqrt( 1 - Z2 / Z1 );

Following are example calculations for a Minimum-Loss Pad.

Z1: 1200 ohm;
Z2: 500 ohm;
LossIndB: 20 log( sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ) ); ~ 8.73

R1: Z1 sqrt( 1 - Z2 / Z1 ); ~ 916.52 ohm
R2: Z2 / sqrt( 1 - Z2 / Z1 ); ~ 654.65 ohm


Z1: 273 ohm;
Z2: 75 ohm;
LossIndB: 20 log( sqrt( Z1/Z2 ) + sqrt( Z1/Z2 - 1 ) ); ~ 10.96

R1: Z1 sqrt( 1 - Z2 / Z1 ); ~ 232.50 ohm
R2: Z2 / sqrt( 1 - Z2 / Z1 ); ~ 88.07 ohm


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