# what are the design of attenuators based upon

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#### abishek

##### Member level 1 calculate t-type attenuator

for t type,lattice type and pi types how are the resistors designed and what is the basis of the design eqns

#### Kral design of attenuators with formulae

abishek,
For the T and Pi type attenuators, you have 3 equations in 3 unknowns.
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The first equation is for the required input resistance in terms of the 3 resistors and the load resistance (specified).
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The 2nd eqauation is for the required output resistance in terms of the 3 resistors and the source resistance (specified).
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The 3rd equation is for the attenuation or gain (specified) in terms of the 3 resistors, the source resistance and the load resistance.
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You solve the 3 simultaneous equations.
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I have not designed a lattice type attenuator, but I think the principle is the same.
Regards,
Kral

#### xxargs

##### Full Member level 4 albert22 said:
Here are a couple of pages on the design of attenuators

h**p://kondor.etf.bg.ac.yu/~tosic/atten.htm
equations:
h**p://www.williamson-labs.com/attenuator.htm

but not so easy to understud and use IMHO...
I find simular in old book:

attenuate for case Z1 = Z2 = Z for unbalanced T-bridge (picture down)

Aritmetic solve:

N = Pin/Pout (for wanted attenuate power ratio - NOT in dB)

first calculate R3

R3 = (2*Z*sqrt(N)) / ( N - 1)

R1 = R2 = Z * ((sqrt(N) -1) / (sqrt(N) + 1))

And IMHO more nice solver method:

Hyperbolic solve:

Z1 = Z2 = Z

gamma = 1/2 ln(Pin/Pout) (for wanted attenuate, here in Neper, 1 Neper = 8.686 dB)

R3 = Z / sinh(gamma)

R1 = R2 = Z * tanh(gamma/2)

and for matching and/or attenuate T-network between different impedances

Z1 <= Z2

aritmetic solve:

check calculate for minimum needed attenuate for match between different impedances:

N = sqr( sqrt( Z1 / Z2) + sqrt((Z1 /Z2) - 1))

if using exact N rate from formula above -> R2 = 0 Ohm

calculate first R3

R3 = (2 * sqrt( N*Z1*Z2)) / ( N - 1 )

R1 = Z1 * ((sqrt( N) -1) / (sqrt( N) + 1) - R3
R2 = Z2 * ((sqrt( N) -1) / (sqrt( N) + 1) - R3

... and more nice hyperbolic form:

check minimum attenuate ratio for impedance match:

gamma = acosh (sqrt(Z1 / Z2))

and if using exactly gamma value from formula above -> R2 = 0 Ohm

calculate R3 first:

R3 = sqrt(Z1 * Z2) / sinh(gamma)

R1 = Z1 / (tanh(gamma) - R3)

R2 = Z2 / (tanh(gamma) - R3)

if R going negative value - use for low attenuate value, incrase attenuate or use amplifier to simulate negative resistance ;-)!

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... and so on for different bridge with same or different impedances port

(little for much me to written all this case here, special TEX-support for nice formula seems broken now - or I not know to use... )

but, if needs formula for PI-network, yell here -------

hyperbolic formula can handle complex impedances compare to aritmetic formula and uses inside of more advanced electrical simulators and impedance calculators for RF circurits.. - and looks more nice and handles easier compare to aritmetic solution.

(but, if case of complex loads, needs complex support on math function as sinh, cosh, tanh, ln and y^x etc. - ...have MS Excel complex math support yet ??)

Calculator HP42S have complex support on all math funktions, and search of 'free42' (hp42S simulator) on google if you like to try replacement of MS-calculator to calculator with full and easy handle complex support on your PC!!!.

/xxargs

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