Why Front-End Loss Before the LNA Costs Sensitivity
A passive loss of L dB ahead of the first gain stage adds L dB to the system noise figure. With a 1.5 dB switch and filter loss, a 1.31 dB cascade becomes 2.81 dB, while putting the LNA first gives 1.48 dB.
For practitioners
Loss in front of the LNA is noise
A passive lossy element, such as a switch, a filter or a trace, attenuates the signal. It also adds thermal noise. For a matched passive element at the reference temperature T0 = 290 K (about room temperature), the two effects combine into one simple rule: the noise figure in dB equals the loss in dB.
So a 1.5 dB switch-plus-filter path has a noise figure of 1.5 dB. In linear terms its noise factor is F = 10^(1.5/10) = 1.413, and its gain is 1/1.413 = 0.708.
The practical consequence is that every tenth of a dB of loss ahead of the first active stage goes straight into the system noise figure. This article shows why with a cascade calculation.
The Friis formula
For a chain of stages with noise factors F1, F2, F3 and gains G1, G2, in linear terms:
Each later stage is divided by the total gain ahead of it. A high-gain first stage therefore hides the noise of everything after it. A lossy first stage has a gain below 1, so it does the reverse. It makes every later stage count for more.
When the first stage is a passive element with loss factor L (a number above 1), then F1 = L and G1 = 1/L. If the rest of the chain has noise factor Frx, the Friis formula reduces to:
In dB this is NF = Loss + NFrx. That is the "dB for dB" result.
Simplest case: loss plus a 2 dB receiver
Take a 1.5 dB loss followed by a receiver with a 2 dB noise figure. The total noise figure is 1.5 + 2 = 3.5 dB. The receiver did not change, but the system is 1.5 dB noisier.
A loss of 3 dB corresponds to a power ratio of about 2 (10^0.3 = 1.995). With 3 dB of loss ahead of the receiver, the noise factor of the receiver is multiplied by about 2. This explains how quickly the penalty grows.
Worked cascade: loss first or LNA first
Now include an LNA with a gain of 15 dB and a noise figure of 1 dB. The following block has a noise figure of 6 dB. The loss is 1.5 dB. Linear values:
- LNA: G = 10^1.5 = 31.62, F = 10^0.1 = 1.259
- Next block: F = 10^0.6 = 3.981
- Loss: L = 1.413, gain 0.708
Loss first, then LNA, then the next block:
F = 1.413 + (1.259 − 1)/0.708 + (3.981 − 1)/(0.708 × 31.62) F = 1.413 + 0.366 + 0.133 = 1.911
That is 10 log10(1.911) = 2.81 dB.
LNA first, then loss, then the next block:
F = 1.259 + (1.413 − 1)/31.62 + (3.981 − 1)/(31.62 × 0.708) F = 1.259 + 0.013 + 0.133 = 1.405
That is 10 log10(1.405) = 1.48 dB.
The difference between the two orders is 2.81 − 1.48 = 1.33 dB. The same parts in a different order change the noise figure by more than a dB.
Why it is dB for dB
Remove the loss from the loss-first case and the cascade is LNA plus next block:
F = 1.259 + (3.981 − 1)/31.62 = 1.353, which is 1.31 dB.
Add the 1.5 dB loss in front and the total becomes 2.81 dB. That is exactly 1.31 + 1.5. This is the result F = L × Frx from the formula above, shown with numbers.
The LNA gain cannot help here. Gain only divides the noise contributions that come after it. The loss sits before the gain, so nothing divides it. The signal and the noise added by the loss are already combined when they reach the LNA.
When the LNA is placed before the loss, the loss lands in the second term, divided by G1 = 31.62. Its contribution falls from 0.413 to 0.013 in noise factor terms. This is the point of the fact that placing the LNA before the lossy element lets the LNA gain reduce the effect of the later loss on noise.
The "almost" in "almost dB for dB" comes from reality. The exact rule assumes a matched element at 290 K. A part at another physical temperature or with a mismatch will deviate somewhat. Treat it as a very good first estimate.
What it does to the signal levels
The level view shows the same chain in dBm. A −90 dBm input signal passes through −1.5 dB, +15 dB and −2 dB:
The levels are −90 → −91.5 → −76.5 → −78.5 dBm. The signal falls by 1.5 dB before it reaches the LNA. The thermal noise at the input does not fall by the same amount, because it is set by the source temperature, not by the signal level. The result is a lower signal-to-noise ratio entering the amplifier, and no later gain restores it. The post-LNA cable loss of 2 dB matters far less, because by that point the signal is 15 dB higher.
Why designers fight for every tenth
Because the penalty is dB for dB, any loss ahead of the LNA counts at full value. Receiver sensitivity is set by the noise floor, which is −174 dBm/Hz at 290 K plus 10 log10(bandwidth) plus the noise figure. The required SNR is then added. When the noise figure rises by 1.5 dB, sensitivity worsens by 1.5 dB for the same bandwidth and required SNR.
A tenth of a dB sounds small, but 0.1 dB of loss is a factor of 10^0.01 = 1.023. That is a 2.3 percent increase in noise factor, and it is paid on every frequency band, in every product, forever. Meanwhile the front end must also select the band, route the antenna and protect the receiver. Each of those jobs wants a filter or a switch ahead of the LNA. The designer's task is to give each of them as little loss as possible and to move the LNA as close to the antenna as the other requirements allow.
Rule of thumb: for passive loss ahead of the first gain stage, add the loss in dB straight onto the noise figure. For loss after a high-gain stage, divide it by the gain first.
In plain words · for students and beginners
Front-end loss in plain words
An everyday analogy
Imagine you are listening for a whisper in a noisy room. If you put a thick curtain between you and the speaker, the whisper gets quieter. The room noise you hear stays the same. Now you hold up a hearing aid. It makes both louder, but it cannot bring back what the curtain took away.
A better plan is to put the hearing aid before the curtain. Then the whisper is already loud when it meets the curtain, and the curtain matters much less.
The analogy breaks down in one place. A real lossy part does not only hide the signal. It also adds a little noise of its own, because it is warm. That is why the noise figure of a lossy part equals its loss.
The same example in simple steps
- A switch and a filter together lose 1.5 dB of signal. A part that loses 1.5 dB of signal also has a noise figure of 1.5 dB. (Noise figure is how much worse the signal-to-noise ratio gets, measured in dB.)
- The amplifier chain behind them (an LNA plus the following block) has a noise figure of 1.31 dB on its own. (An LNA is a low-noise amplifier, the first amplifier in a receiver.)
- Put the loss first. The noise figures add: 1.5 + 1.31 = 2.81 dB.
- Put the LNA first and the loss after it. The total is only 1.48 dB.
- The same parts in a different order differ by 1.33 dB.
Here is how the signal level moves through the chain. Gains and losses in dB are simply added to a level in dBm (decibels relative to one milliwatt).
Mistakes beginners make
- Adding more gain to fix the loss. More gain behind the loss does not recover the lost signal-to-noise ratio. It raises signal and noise together.
- Treating the loss as only a level problem. Loss before the LNA lowers the signal and also raises the noise figure. Both hurt sensitivity.
- Ignoring small numbers. A tenth of a dB looks tiny. It is still a 2.3 percent change in noise factor, and it adds up with every other small loss in the path.
- Adding noise figures in dB for any chain. Dividing by gain only works in linear numbers. In dB, simple addition holds for a passive loss in front of a receiver, not for an amplifier chain.
Remember
- A passive loss of L dB ahead of the first amplifier adds L dB to the system noise figure.
- Gain only helps against noise that comes after it, so put the LNA as early as the design allows.
- Sensitivity gets worse by the same number of dB as the noise figure, so every tenth of a dB counts.
Related pages on RF View
Frequently asked questions
Why does loss before the LNA hurt noise figure more than loss after it?
Loss before the LNA adds its noise factor directly to the first term of the Friis formula. Loss after the LNA is divided by the LNA gain, so its effect is largely suppressed.
What is the noise figure of a passive attenuator or filter?
For a matched passive element at the reference temperature T0 = 290 K, the noise figure in dB equals its loss in dB. A 1.5 dB loss has a 1.5 dB noise figure.
How much sensitivity do I lose from 1 dB of insertion loss before the LNA?
About 1 dB. Total noise figure rises by the loss in dB, and receiver sensitivity worsens by the same amount for a given bandwidth and required SNR.
Why not just add more LNA gain to make up for front-end loss?
Gain after the loss cannot recover the signal-to-noise ratio already lost. The noise added by the loss is already mixed into the signal, so more gain amplifies both equally.