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Element_115
Joined: 23 Mar 2002
Posts: 312
Helped: 21
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 07 Dec 2004 10:05 Image Reject ratio derivation |
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Does anyone know where I can find the derivation to these eqations:
IRR(phase)= 1 +4(cot(Δφ))²≈ 4/{(Δφ)²}
IRR(gain) ={(A+B)/(A-B)} = [{1+(1+ε)}/{1+(1+ε)}] ≈ 4/ε²
IRR(total) ≈ 4/{(Δφ)² + ε²}
These EQ's are in Thomas Lee's book "Design of RF CMOS IC"
2nd edition pg702
If anyone could explain how or refer me to some papers it would be greatly
appreciated.
Thanks in advance
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dazhen
Joined: 23 Nov 2004
Posts: 60
Helped: 2
Location: In the Mountain
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| 07 Dec 2004 19:13 Re: Image Reject ratio derivation |
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Equation 1
IRR(phase) = 1 +4(cot(Δφ))² = 1+4[cos(Δφ)/sin(Δφ)]² ≈ 1+4{[1-(Δφ)²/2]/Δφ}²
≈ 1+4[1-(Δφ)²]/(Δφ)² = 4/{(Δφ)²}-3 ≈ 4/{(Δφ)²}
Equation 2 seems not right. You may key in something wrong.
Apply 1/IRR(total) = 1/IRR(phase) + 1/IRR(gain), you can easily obtain equation 3.
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flatulent
Joined: 19 Jul 2002
Posts: 4856
Helped: 292
Location: Middle Earth
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| 07 Dec 2004 20:37 Re: Image Reject ratio derivation |
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| Try drawing a vector diagram and then with the error terms calculate the portion of the nominally orthogonal vectors that each project onto the other one.
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