Mathcad - ee217projtodonew2.mcd

n is the noise resistance representing the portion of V neq
2 which is uncorrelated with I neq
2.
It is always less than R n , and in the case where the noise is 100% correlated, it is equal to 0.
r n N, I C
, s R n N, I C
, s . 1 γ N, I C
, s r n N, I C
, s 5.943 Ω
2
= Correlation Resistance
G n is the noise resistance representing the portion of I 2 neq which is uncorrelated with V neq
2.
It is always greater than g n , and in the case where the noise is 100% correlated, it is equal to
infinity.
2
G n N, I C
, s g n N, I C
, s . 1 γ N, I C
, s
1
G n N, I C , s
Optimal Noise Figure and Source Impedance
= 508.546 Ω Correlation Conductance
The optimal source resistance is then given by the following equation, using admittance or
impedance noise parameters. Both cases should given the same answer.
Z nopt N, I C , s
r n N, I C , s
g n N, I C , s
Z nopt N, I C , s = 54.761 4.823i ohm
Re Z corr N, I C , s
2
. Optimal Source Impedance
for Minimal Noise Figure
jImZ corr N, I C , s
In the special case, where the noise of the following stages dominates, the optimal noise
source impedance will equal the optimal power source impedance. In the special case, where the
noise of the following stages is zero, the optimal system source impedance will equal the optimal
device source impedance. An optimal system noise figure can be derived by cascading an
infinite number of identical devices and finding the optimal source impedance. Friis explored this
ideal to derive and optimal system source impedance given a single device charateristics. In
reality, all of the devices in a receiver chain will not be the same for distortion purposes.
NF min N, I C , s 10.
log 1 2.
g n N, I C , s . Re Z corr N, I C , s
...
+
g n N, I C , s . r n N, I C , s g n N, I C , s Re Z corr N, I C , s
.
2
NF min N, I C , s = 0.949 dB
Optimal Noise Figure
Noise figure will also be increased by a jammer a frequency offset from the desired signal
f off +f desired , mixing with bias noise at the same offset at basband, f off . This derivation is breifly
described in the Mathcad file: biasnoise.mcd.