S Parameters

S Parameters_Sheet 1 of 11

S-PARAMETERS Scattering Matrix

V1i

V2i

I1

I2

V1
V1r

Z01

Z02

V2
V2r

t1
Input T.L L1=0 V1 = V1i + V1r

Reference planes

t2
Output T.L L2=0 V2 = V2i + V2r

Define normalised voltages a1 =
Note Using normalised voltages ≡ making the characteristic impedances =1

V1i Z 01 V1r Z 01 V2i Z 01 V2r Z 01
a2

b1 = a2 = b2 =

a1

b1

b2

t1
Outgoing voltage waves ∝ ingoing voltage waves .

t2

b1 = S11 . a1 + S12 . a2 b2 = S 21 . a1 + S 22 . a2 S11 S12 a1 b1 b2 = S21 S22 a2
Scattering Matrix

Sheet 2 of 11

Measurement of S11 & S12 (1) Apply input to Port 1 , terminate at Port 2 with a Matched Load ∴a2 = 0.

∴ S11 =

b1 = reflection coefficient at Port 1 (matched load at Port 2). a1 a2=0 b2 = Voltage transfer ratio Port 1 to Port 2 (matched load at Port 2). a1