# Y Parameters

Y Parameters are commonly used 2 port admittance parameters. Their usage has largely been replaced by the usage of S parameters. However older datasheets characterize components in terms of Y parameters.

## Y Parameters to S Parameters Conversion

Y parameters can be converted to S parameters using the following formulae:

Y11 = ( (1 + S22)(1 - S11) + (S12 * S21) )

-----------------------------------------

( (1 + S11)(1 + S22) - (S12 * S21) ) * 50

Y12 =            -2 * S12

-----------------------------------------

( (1 + S11)(1 + S22) - (S12 * S21) ) * 50

Y21 =            -2 * S21

-----------------------------------------

( (1 + S11)(1 + S22) - (S12 * S21) ) * 50

Y22 = ( (1 + S11)(1 - S22) + (S12 * S21) )

-----------------------------------------

( (1 + S11)(1 + S22) - (S12 * S21) ) * 50

## Y Parameter Interpolation

They are specified for a few frequencies on the data sheet of the RF part. To get at the Y parameter for any intervening frequency we should ideally measure it. Such measurements are often time consuming and expensive. We can approximate the Y parameters for a frequency given the Y parameter for two frequencies in the datasheet.

The Y parameter has a real part and an imaginary part, and interpolation for each of them must be carried out separately.

The real component usually varies linearly, so for real values you may use

real value at frequency F=

real value at lower frequency +

F - lower frequency

------------------------------------------------- *

higherfrequency - lower frequency

(real value at higher freq - real value at lower freq)

The imaginary component varies as a ratio of frequencies so

Imaginary component at frequency F =

imaginary at lower frequency *

(frequency/lower frequency)

-----------------------------

(high frequency/low frequency)

*

(imaginary value at high frequency)

-----------------------------------

(imaginary value at low frequency)

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