How to measure sensitivity of receiver with LNA?

[KAGAN]

Hello everyone,
I designed a LNA with 868MHz center frequency. I want to use this LNA as a RF Receiver front end. The receiver has also the same center frequency.
Receiver has -55dBm sensitivity i want to increase it. So my target specifications is S21>=20dB, NF>20dB, S11 and S22<-10dB and all of this requirements are valid between 857-947MHz frequency range. So that i guess my LNA has a bandwidth of 90MHz. So i know there is a formula for receiver sensitivity -174+NF+10log(BW)+SNR. But i have no idea about SNR. I designed this LNA with Advanced Design System. So i have 2 questions. The logic behind the bandwidth is correct? and How can i measure SNR in this formula? or is there another method i can use for calculate receiver sensitivity?

--- Updated Mar 13, 2022 ---

Hello everyone,
I designed a LNA with 868MHz center frequency. I want to use this LNA as a RF Receiver front end. The receiver has also the same center frequency.
Receiver has -55dBm sensitivity i want to increase it. So my target specifications is S21>=20dB, NF>20dB, S11 and S22<-10dB and all of this requirements are valid between 857-947MHz frequency range. So that i guess my LNA has a bandwidth of 90MHz. So i know there is a formula for receiver sensitivity -174+NF+10log(BW)+SNR. But i have no idea about SNR. I designed this LNA with Advanced Design System. So i have 2 questions. The logic behind the bandwidth is correct? and How can i measure SNR in this formula? or is there another method i can use for calculate receiver sensitivity?

I am sorry i wrote NF wrong. It should be NF<2dB

 

[BigBoss]

NF=20dB is too much.
SNR depends on the modulation. For instance SNR=10-12dB can be acceptable for FM. For others, refer to specifications.
SNR can either be added to formula as you wrote or measured. Instead, EVM can also be used or BER is also metric of a sensitivity of the system. So there are few definitions for such purposes.

 

[KAGAN]

NF=20dB is too much.
SNR depends on the modulation. For instance SNR=10-12dB can be acceptable for FM. For others, refer to specifications.
SNR can either be added to formula as you wrote or measured. Instead, EVM can also be used or BER is also metric of a sensitivity of the system. So there are few definitions for such purposes.

I am sorry, i just wrote NF wrong. My noise figure is 1.95dB. I want to design a Wake up Receiver so that i am using OOK Modulation technique. SNR can be measured but i just don't know how to do it ADS. I know my signal power at the input but how can i measure the noise power at the input by using Advance Design System. Is there a tool and how to use it?

And a second question i add the receiver that i want to increase sensitivity. Like i said it has -55dBm sensitivity. There is one thing i am wondering about. If i give -78dBm input power at the input of my LNA i take -55dBm output power at the output of it and this is the weakest signal power that WUR in the attach file can accept. Can i say if i connect LNA to the receiver i increase sensitivity of it to -78dBm or this is wrong idea. If it is correct my SNR should be 14dB is it acceptable for it?

 

[vfone]

The bandwidth BW in your sensitivity formula is not 90MHz.
90MHz is the receiver frequency range, and perhaps you can name also the LNA bandwidth.
The BW in the sensitivity equation is the channel bandwidth, which for OOK modulation is between 2kHz and 16kHz.
Doing the math for BW=16000Hz, NF=2dB, and SNR=14dB, you get -116dBm receiver sensitivity, which is pretty close to most of the ISM 868MHz chipsets on the market.
With the given data, I think you can decrease the SNR requirements even down to 10dB, and the system still works fine.

 

[KAGAN]

The bandwidth BW in your sensitivity formula is not 90MHz.
90MHz is the receiver frequency range, and perhaps you can name also the LNA bandwidth.
The BW in the sensitivity equation is the channel bandwidth, which for OOK modulation is between 2kHz and 16kHz.
Doing the math for BW=16000Hz, NF=2dB, and SNR=14dB, you get -116dBm receiver sensitivity, which is pretty close to most of the ISM 868MHz chipsets on the market.
With the given data, I think you can decrease the SNR requirements even down to 10dB, and the system still works fine.

Thank you for clearification about the BW. I got it. But about SNR i did not measure it i just said that because of the receiver i attached has -55dBm and when i give input power of -78dBm to my LNA i got output power of -55dBm and i am giving this output power to the receivers input. (But i thought there my BW=90MHz) so when i use the values -174+1.95dB+10log(90x10^6)+SNR=-78dBm so that SNR should be 14dB. This is just reasoning.

From what you said ''With the given data, I think you can decrease the SNR requirements even down to 10dB, and the system still works fine.'' why you think that SNR could be decrease to 10dB?

 

[vfone]

SNR (signal to noise ratio) is a receiver system requirement usually measured before the demodulator.
Different modulation types, FM, AM, OOK, BPSK, QPSK, etc., have different requirements for SNR (see the attached plot for bit error rate vs SNR).
As you see (for a given bit error rate) the SNR for OOK is about 10dB to 14dB for a BER of 10^-3 to 10^-6. Now depends for what BER is looking your system.
In a receiver, lowering the NF or decreasing the BW, will relax the SNR requirement.