System Balance
In order to verify that the system requirements are met, it is necessary to calculate the gain, NF and OIP3 budget. In this sense, having the specifications of each system block, it is possible to calculate the cascaded system parameters.
Cascaded Gain
Provided that each block is matched, the system gain is equal to the product of the blocks' gain in natural units (the sum in dB):
$$ G_{system} = { \prod_{i=1}^{n} g_i^{(n.u.)}} = { \sum_{i=1}^{n} G_i^{(dB)}} \tag{1} $$
Noise Figure
The following equation relates the system noise figure with the NF of each block:
$$ NF_{system} = NF_1 + { \sum_{i=2}^{n} \frac {NF_i^{(n.u.)}} {\prod_{k = 1}^{i-1} g_{k}^{n.u.}}} \tag{2} $$
It is important to note that the insertion loss of any passive block before the first stage is directly added to the system NF. Consequently, the system designer must minimize loss at the input.
OIP3
The cascaded OIP3 depends on the phase of the intermodulation products. In general, the designer should consider the case where the intermodulation products are in-phase since the IMD will be maximum.
$$ OIP3_{system} = \frac{1}{\frac{1}{g_{n} · OIP3_{n-1}} + \frac{1}{OIP3_n}}\tag{3} $$
As shown in Eq. (3), the system OIP3 is limitted by the block with the highest OIP3, but it may be lower if the PA is not properly driven. Also, it is important to Notes that, despite the fact that passive blocks have a very high IP3, their insertion loss reduces the available IP3 at the output.
Summary
- Avoid lossy blocks at the input since it adds up to the system NF.
- Avoid lossy blocks at the output since it reduces the system OIP3
- If lossy interstage blocks are used, ensure that the last amplifier is properly driven, otherwise the system may exhibit less OIP3 than that specified by the PA.
References
[1] William Egan, Practical RF System Design. John Wiley and Sons, 2003. ISBN 0-471-20023-9
[2] P. Vizmuller, RF design guide: systems, circuits, and equations. Boston u.a.: Artech House, 1995.