Noise Figure

Sensitivity in a receiver is normally taken as the minimum input signal

with specified signal-to-noise ratio(SNR) ratio[1-2]. As illustrated in following

formula :

Nevertheless, what a system (board level) RF engineer can improve is only noise

figure. The definition is shown in the following formula :

SNR is the more the better, if ideal, SNR is infinite(it means that there is

completely no noise). But in reality, there must be noise. Thus, noise figure is a

measure of degradation of the SNR, caused by components in a RF signal chain.

1

If the signal has 1dB SNR degradation after passing through the component, we

can say noise figure of the component is 1dB.

As illustrated in following figure, it is impossible for noise figure to be negative,

which indicates that output SNR is the same as input SNR at best. In other words,

when the signal passes through a component, whether active or passive, the

output SNR merely decreases, never increases. Consequently, the minimum noise

factor is 1.

2

Therefore, the more components the signal passes through, the more SNR

degrades.

Nevertheless, whether the component is active or passive, noise figure is due to

its insertion loss.

3

Of course, in active state, the amplifier has only gain, no insertion loss. Even if so,

the SNR still degrades merely after passing through an amplifier. After all, as

mentioned above, the output SNR of signal never increases after passing through

a component, and noise figure is never negative. Let’s illustrate the concept

further in the following figure :

As illustrated in the above figure, ideally, the output SNR remains the same after

passing through a LNA, because the signal and noise amplify simultaneously with

same gain. But, LNA has additive noise from itself, which increases noise floor. So

output SNR decreases. Take one LNA, RF2815 of RFMD , for example, noise figure

is 0.85 dB, it indicates the additive noise is 0.85 dB, and SNR degrades 0.85 dB

after passing through the LNA [3].

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Noise Figure and Sensitivity

Since SNR merely degrades after the signal passes through a LNA, why can the

external LNA (eLNA) improve sensitivity ? Let’s take a case for illustration :

The formula of cascade noise figure :

Let’s calculate the cascade noise figure in the case without eLNA :

5

6

And let’s calculate the cascade noise figure in the case with eLNA :

According to [4-6], how much cascade noise figure decreases is equivalent to

how much sensitivity improves. Thus, with eLNA, cascade noise figure decreases

about 3 dB (5.04 – 2 = 3.04), it means that sensitivity improves about 3 dB as

well.

7

As mentioned above, all components, whether active or passive, even layout trace

or amplifier, all have noise figure. Consequently, the SNR of Rx signal must

degrade in the path from antenna to receiver. So we simplify the above two cases

as following figure :

Noise figure of eLNA degrades SNR, though. Nevertheless, at least, it can mitigate

the SNR degradation. In other words, with eLNA, SNR degrades necessarily;

without eLNA, SNR degrades more. As illustrated in above cases, with eLNA, SNR

degrades 2 dB; without eLNA, SNR degrades 5.04 dB. That is to say, with eLNA,

the SNR degradation is from 5.04 dB to 2 dB, which amounts to 3 dB

improvement. Owing to this analysis, eLNA does improve sensitivity.

8

From the calculation of the above cases, we realize that eLNA weakens the

contributions that the stages subsequent to eLNA make to cascade noise figure.

Thus, for convenience, we can ignore the stages subsequent to eLNA while

calculating cascade noise figure.

From above analysis, for the cascade noise figure calculation, we just need to

focus on the stages preceding eLNA and eLNA itself. As mentioned above,

whether the component is active or passive, noise figure is due to its insertion

loss. Therefore, according to cascade noise figure formula :

the total insertion loss of these stages preceding eLNA is just F1. If we simplify

the cascade noise figure calculation further, merely add F1 and eLNA noise figure

together, and compare the result with previous calculation :

As shown in above table, the calculation of simplified method is almost in concert

with previous calculation. Consequently, we can simplify the cascade noise figure

calculation as following formula :

Noise Figure(dB) = eLNA Pre-loss(dB) + eLNA Noise Figure (dB)

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LNA, as its name implies, has low noise figure. For example, RF2815 of RFMD, is

only 0.85 dB, and BGA7L1N6 of Infineon is only 0.6 dB. Thus, we can conclude

that eLNA pre-loss nearly dominates cascade noise figure. That is to say, if eLNA

pre-loss increases 1 dB, the sensitivity degrades 1 dB directly.

So, according to previous cases, we put eLNA in the wake of ASM so that we can

ignore the the contribution that long layout trace makes to cascade noise figure.

In other words, we decrease eLNA Pre-loss, and then improve sensitivity. As

illustrated in following figure :

10

If we put eLNA as the following figure :

the sensitivity doesn’t improve anymore because eLNA Pre-loss doesn’t decrease.

Unless, noise figure of internal LNA (iLNA) is much larger than which of eLNA so

that sensitivity improves because of ignoring the contribution that iLNA makes to

cascade noise figure (because iLNA follows eLNA). Consequently, where you put

eLNA does affect how much sensitivity improves. Of course, the closer to antenna,

the more sensitivity improves.

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In cellphone, we may make GPS antenna be far away from 2G/3G/4G main

antenna to isolate GPS weak signal from other RF signals. As shown in following

figure :

That is to say, the GPS antenna will be far away from receiver, and sensitivity

degrades very much. It’s also the reason why GPS is the RF function that we use

eLNA most often[7]. Thus, we should put GPS eLNA close to GPS antenna, the

closer the better. Otherwise, the large eLNA Pre-loss due to long layout trace

degrades sensitivity. As a result, eLNA can’t help us improve sensitivity anymore.

As illustrated in following figure :

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In order to decrease eLNA Pre-loss due to layout trace, in addition to shortening

its length from antenna to eLNA, if necessary, we can clear the metal below the

microstrip trace further to widen its width without affecting the expected 50 /

100 Ohm [8].

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While selecting these components in front of eLNA, e.g. ASM, SAW filter etc. ,

their insertion loss should be as small as possible. For example, there usually are

pre-SAW and post-SAW in GPS application, and low insertion loss

is the key point of pre-SAW.

Besides, the SAW filter locates between LNA and mixer in some receivers to avoid

degrading sensitivity because of the insertion loss of SAW filter.

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In addition, eLNA Pre-loss includes not only insertion loss, but also mismatch

loss. Therefore, to do impedance matching is due to decreasing mismatch loss,

then improves sensitivity further.

If necessary, you can even tune the source-pull of eLNA to the location with

minimum noise figure in Smith Chart.

Nevertheless, for convenience, we still usually tune the source-pull to around

50 Ohm(single-end) or 100 Ohm (differential pair) in Smith Chart.

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As mentioned above, eLNA pre-loss nearly dominates cascade noise figure.

Nevertheless, if we can reduce eLNA noise figure further, the sensitivity still

improves more or less. As illustrated in following figure, the more Vcc of LNA is,

the lower noise figure of LNA will be [9].

Generally speaking, there is a series inductor or bead in Vcc of LNA as the RF

choke to suppress high frequency noise in Vcc. However, the internal resistance

within inductor or bead should not be too large, and Vcc layout trace should not

be too long or too thin. Because these factors cause IR drop, and then decrease

Vcc of LNA and increase noise figure of LNA.

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As for eLNA gain, we realize that more gain cause lower cascade noise figure [7] :

But, more gain cause lower IIP3 as well [7] :

17

According to [7], we realize that the eLNA gain is a trade-off between linearity

and sensitivity,

and poor linearity leads to poor sensitivity as well. Thus, the eLNA gain is neither

the more the better nor the less the better. It should be the more exact the better.

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Besides, lower gain doesn’t lead to poorer sensitivity necessarily. We take

RTR6285A and WTR1605L of Qualcomm for example. As shown in following

table, comparing with RTR6285A, gain of WTR1605L is lower, but noise figure of

which is not higher.

And according to the following measurement , WTR1605L with lower gain has

better sensitivity than RTR6285A with higher gain:

It indicates that if both LNA and mixer have lower noise figure, even with lower

gain, the cascade noise figure can still be low to achieve better sensitivity.

Nevertheless, it depends on the receiver design.

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eLNA within RF switch

We take BCM4356 of Broadcom

As shown in above figure, we need a RF switch to switch the three paths of

Tx / WiFi Rx / Bluetooth

bypass mode, and the sensitivity measurements are as below :

Thus, we may conclude that sensitivity degrades about 15.5 dB without eLNA.

Nevertheless, the conclusion is wrong.

eLNA within RF switch

We take BCM4356 of Broadcom for illustration [10] :

As shown in above figure, we need a RF switch to switch the three paths of

Tx / WiFi Rx / Bluetooth separately. The RF switch integrates an eLNA, which has

bypass mode, and the sensitivity measurements are as below :

Thus, we may conclude that sensitivity degrades about 15.5 dB without eLNA.

Nevertheless, the conclusion is wrong.

As shown in above figure, we need a RF switch to switch the three paths of WiFi

. The RF switch integrates an eLNA, which has

Thus, we may conclude that sensitivity degrades about 15.5 dB without eLNA.

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As shown in above figure, both a RF switch integrating eLNA with bypass mode

and a simple SP3T don’t amplify the signal. But, they have different insertion loss,

the difference is about 6 dB. In other words, if we put a simple SP3T instead of a

RF switch integrating eLNA with bypass mode, sensitivity degrades about 9.5 dB

(15.5 – 6 = 9.5) merely. Consequently, to be accurate, sensitivity degrades about

9.5 dB without eLNA, not 15.5 dB.

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Conclusion

For eLNA pre-loss :

1. Layout trace should be short and wide (without affecting the expected 50

Ohm or 100 Ohm)

2. Select those components with less insertion loss

3. Tune the source-pull of eLNA to 50 Ohm(single-end) or 100 Ohm (differential

pair), or to the location with minimum noise figure in Smith Chart

For eLNA itself

1. Select the eLNA with lower noise figure

2. Select the eLNA with exact gain, neither too large nor too small

3. Avoid IR drop in Vcc of eLNA

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Reference

[1] RECEIVER SENSITIVITY / NOISE

[2] Receiver sensitivity

[3] LNA Products for GPS and Cellular Applications, RFMD

[4] LTE LNA and Module, Infineon

[5] Guidelines for achieving best-in-class RX Diversity Performance in your

Smartphone Applications

[6] Understanding and Enhancing Sensitivity in Receivers for Wireless

Applications, TEXAS INSTRUMENTS

[7] Sensitivity or selectivity -- How does eLNA impact the receriver performance,

slideshare

[8] Fundamentals of PCB Layout Guidelines for radioOne® Designs, Qualcomm

[9] A Single Chip Silicon Bipolar Receiver for GPS/GLONASS Applications,

MAXIM

[10] Single-Chip 5G WiFi IEEE 802.11ac 2×2 MAC/Baseband/Radio with

Integrated Bluetooth 4.1, FM Receiver, and Wireless Charging, Broadcom

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