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Local Oscillator-frequency choosing

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jason_class

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Hello All

I am thinking of some basic question about LO and I cant figure it out
I need your help to give me some explanation so I can further investigate my text book.

Say there are 3 signals [frequency at wo-k, wo, wo+k]going into the input of a LO. Then due to the nonlinearity of LO, we get Intermodulation harmonics terms. If wo is the desired frequency while the other two are interferers, my question is at which frequency Local Oscillator will tune at?

For any theoritical and practical purposes, what is the method to find the oscillator frequency and/or period?

Maybe this question sounds too general. Therefore, if you have any further details to complement this question and doubts, kindly share your views.
Thank you

rgds and thanks
Jason
 

toonafishy

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You would put these signals into a mixer. You also put the LO signal into the mixer. You choose the LO frequency to get the desired frequnecy out of the mixer. The mixer output will be LO+wo and LO-wo. So one of these must be your desired output frequency. The mixer will also put out L0 +/- (wo+k) and LO +/- (wo-k). These are not intermodulation but products of the natural mixing pocess.
 

brmadhukar

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The LO is fixed.
you get harmonics and images. You need to filter these out usig the filters.
brmadhukar
 

jason_class

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Thank you All

This confused me.
The Intermodulation and mixing products, aren't they the same?
If they are not the same, at which output or which circuit component, we have each of the IM and mixing product?
Should I say mixing product happened during "mixing" in mixer and we get them at the mixer's output?
Then Intermodulation is something already present before mixer? Why so?

Anyone , please enlighthen

rgds and thanks
Jason
 

RFDave

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In many respects, the difference between intermoduation and mixing is that mixing is desired, and intermodulation isn't.

Generally, intermodulation refers to a 3rd order mixing term in an amplifier stage, where you have two frequencies at W1 and W2 present at the input. At the output, you end up with signals at W1, W2, 2*W1-W2 and 2*W2-W1. This is a problem with closely spaced W1 and W2, because the 2*W1-W2 and 2*W1-W2 frequencies are close in frequency to W1 and W2, and so they are difficult to filter out.

In a Mixer, typically you have W1 present at the input, along with W2 Present at the LO Port. At the output, you have W1-W2 and W1+W2 frequency terms. This is a 2nd order non-linearity, not a 3rd order non-linearity.

Because they are different order non-linearities, you can optimize stages for one behavior or another, because they are governed by different processes. Things that you use for Mixers typically have a strong 2nd order non-linearity, and you don't really care about the 3rd order non-linearity, since you can filter out the intermodulation products, they are different in frequency from the Intermodulation products.
For amplifiers, you generally don't worry about a second order non-linearity, since you can filter out the different frequencies, but the Intermodulation terms can show up in band and cause you trouble, so you want something with a small third order nonlinearity.


Dave
 

jason_class

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Hi Dave

Thank you so much
That is something I really wish to confirmed about. Your explanation is indeed convincing.
Can I summarise as
1) IM (third order non-linearity) happens in amplifier such as LNA
2) 2nd order nonlinearity is associated with mixer
3) SO when LNA and signal from LO are "mixed" together, the non linear terms(including 3rd order) from LNA are mixed nonlinearly with signal from LO with 2nd order nonlinearity for those input terms

Correct me if I am wrong, please

Can I say Gilbert cell mixer is also having the non linearity up to 2nd order term?

Kindly enlighthen
Thank you

rgds and thanks
Jason
 

devtel

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If the input signal is coming in with two closely spaced channels, say at ω and
ω + δ, then the third order IM terms of interest are

2 ω - ( ω + δ ) = ω - δ

and

2 ( ω + δ ) - ω = ω + 2δ

My question is, are both of these frequencies important for IM distortion, or is it only the first one, which is nearest to ω that causes problems ?

For multitone input, say N tones, each spaced by δ, so that we have ω, ω + δ,
ω + 2 δ, ω + 3 δ, ..., ω + N δ, we will get many 2 tone and 3 tone IM products

2 (ω + i δ) - ( ω + j δ ) = ω + (2 i - j ) δ

and

(ω + i δ) + ( ω + j δ ) - (ω + k δ) = ω + ( i + j - k )δ.

Are the only terms of interest for IM3 the ones where

2 i - j = ± 1

and

i + j - k = ± 1 ?

Thanks

Tel
 

RFDave

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both frequencies are important. FOr example, if the two signal's are seperated by 100 kHz, you will have (assume 21.7 MHz IF Frequencies )

Input:
800.2 MHz (W1)
800.3 MHz (W2)

Output:
800.1 MHz (Lower intermodulation product, 2*W1-W2)
800.2 MHz (W1)
800.3 MHz (W2)
800.4 MHz (Upper intermodulation product, 2*W2-W1)

(Double bonus points for the student who explains what happen's if W1 and W2 are different in amplitude by 1 dB)

At the output of a mixer, assuming LO frequency of 778.55 MHz:

21.55 MHz
21.65 MHz
21.75 MHz
21.85 MHz
Depending on the filter bandwidth, you may or may not be able to ignore the intermodulation products at 21.55 and 21.85 MHz.


Tel, you have determined the frequencies of interest for 3rd order products. The remaining issue is to determine which one's fall in-band.

Dave
 

jason_class

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Since IM3 terms of interest are the ones that fall within the
receiver's bandwidth. I would like to know whether the bandwidth of
the reciever is the same as the channel width(delta) for the following 3 channels that is mixed with a mixer at receiver side? Their relations in mathematical equation?

channels: A1cos(w0-delta)t , A2cos(w0)t, A3cos(wo+delta)t

the term with wo is of interests.

Kindly enlighthen


rgds and thanks
Jason
 

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