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# How to calculate beat signal frequency from delay?

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#### tony_lth

I am curious about the beat signal frequency.
Let's say RF freq is 100M, so its period is 10ns.
LO has the same freq, i.e. 100M, but LO phase is 500ps delayed, that is 1/20 of period.
AFter the mixer, get the beat signal,
1. so how to calculate the beat signal freq from above data?
This is just help me to understand the radar beat signal, not a live system.
2. How this beat signal depend on the phase noise of LO?
Thanks.

#### luben111

Hi,

I guess you're talking about CWFM radars where sending sine wave signal and the beating frequency is a function of the distance to the object.

Notice that you can detect multiple objects simultaneously - they will create different beating frequencies. A FFT is the best way to detect the objects and to estimate the distance to them.

tony_lth

### tony_lth

Points: 2

#### jiripolivka

I am curious about the beat signal frequency.
Let's say RF freq is 100M, so its period is 10ns.
LO has the same freq, i.e. 100M, but LO phase is 500ps delayed, that is 1/20 of period.
AFter the mixer, get the beat signal,
1. so how to calculate the beat signal freq from above data?
This is just help me to understand the radar beat signal, not a live system.
2. How this beat signal depend on the phase noise of LO?
Thanks.

2. Except of very poor LO phase noise, it will not affect the results as the beat frequency is "cleaned" by integration. Range error is defined without any component effect.

tony_lth

### tony_lth

Points: 2

#### tony_lth

Hi, luben111,
From your given link, there is no equation for calculate the beat signal, could you give more details or other links for beat signal calculation?
Best,

- - - Updated - - -

Hi, jiripolivka,
Is there any equation to describe how the poor phase noise can mask the beat signal?
I need equation to calculate to assuare that phase noise can't impact on beat signal.
Thanks.

tony_lth

### tony_lth

Points: 2

#### Attachments

• Frequecy Modulated Continuous Wave (FMCW) Radar.pdf
1.7 MB · Views: 81
tony_lth

### tony_lth

Points: 2

#### FvM

##### Super Moderator
Staff member
The original post is talking about fixed frequency, not FMCW. You don't get a beat frequency by mixing signals of same frequency.

tony_lth

### tony_lth

Points: 2

#### luben111

Hi FvM

I agree with you - in case of fixed frequency he needs just to check for Doppler radar for beating frequency

But in case of fixed frequency the only one thing he could get from beating frequency is the relative speed of the object. In case of FMCW radars he gets the distances and speeds for multiple objects which is more attractive.

Luben

tony_lth

### tony_lth

Points: 2

#### tony_lth

Hi, FvM and luben111 and jiri,
Thank you very much.
Now I have some clear idea about FMCW.
I will think about how to do it.
From China requirements, it seems that FMCW can work at 2400-2483.5MHz or 24-24.25GHz without license approval.
Are these band wide enough for FMCW (83M@2.4GHz and 250M@24GHz)?
And are these band free in other country when using micro-power and short-distance radio equipments?

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