Dec 7, 2004 #1 E Element_115 Advanced Member level 2 Joined Mar 23, 2002 Messages 508 Helped 72 Reputation 144 Reaction score 43 Trophy points 1,308 Activity points 3,755 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
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
Dec 7, 2004 #2 D dazhen Member level 3 Joined Nov 23, 2004 Messages 56 Helped 2 Reputation 4 Reaction score 0 Trophy points 1,286 Location In the Mountain Activity points 437 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.
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.
Dec 7, 2004 #3 flatulent Advanced Member level 6 Joined Jul 19, 2002 Messages 4,624 Helped 489 Reputation 980 Reaction score 151 Trophy points 1,343 Location Middle Earth Activity points 46,689 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.
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.