RF Microelectronics - Basic concepts - nonlinearity
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This document provides an introduction to basic RF concepts including nonlinearity, noise, impedance transformation, gain, linearity and time variance, harmonic distortion, gain compression, cross modulation, and intermodulation. It discusses key effects like how nonlinearity can lead to harmonic distortion and intermodulation distortion, and how gain compression occurs when the input power is increased. It also introduces important RF parameters for characterizing devices and circuits like the 1 dB compression point and third order intercept point.
![Memory-less systems [outputs don’t depend on past values of
input(s), opposite to Dynamic systems.]
Memory-less linear systems
y(t) = x(t)
Memory-less nonlinear systems
y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t)
If j=0 for even j, the system is said to
have odd symmetry, when his
response to –x(t) is negative to that to
x(t).
The circuit having this property is
called differential or balanced.](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-13-320.jpg)
![Nonlinearity effects.
y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t)
DC
component
Total
Gain
[compression
@ 1 3 <0]
2nd
harmonic
Suppresse
d for odd
symmetry.
3rd
harmonic
Small
signal
gain](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-14-320.jpg)
![Gain compression
y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t)
DC
component
Total
Gain
[compression
@ 1 3 <0]
2nd
harmonic
Suppresse
d for odd
symmetry.
3rd
harmonic
Small
signal
gain
@ 1 3 <0 the gain is compressed as A rises
1 =500
3 =-0.1](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-16-320.jpg)
![Gain compression [1-dB compression point]
@ 1-dB compression point, the gain is
reduced by 10%
Desensitization: when large
interferer [blocker] causes gain
compression while sensing weak
desired signal.
[lowers the SNR]](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-17-320.jpg)
![Intermodulation[two-tone test].
Two signals with
small A
is chosen to minimize
nonlinearity effect on it
Gain = 1
Fundamental A
IM products A3
Plot in log-log scale,
the intersection is
the third-order
intercept point
IIP3 is beyond the allowable
input range or even higher
than the supply voltage,
because if the input level
reached the AIP3 the gain
drops and higher order IM
products become significant.](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-21-320.jpg)
![Intermodulation[two-tone test].
IIP3 is chosen beyond the allowable
input range or even higher than the
supply voltage, because if the input
level reached the AIP3 the gain drops
and higher order IM products
become significant.
AIIP3 is greater than
the 1-dB compression
point with 9.6 dB](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-22-320.jpg)
![IIP3 direct calculation. [two-tone test].](https://image.slidesharecdn.com/lecture-1-150317154931-conversion-gate01/85/RF-Microelectronics-Basic-concepts-nonlinearity-23-320.jpg)
RF Microelectronics - Basic concepts - nonlinearity
- 1. RF Microelectronics CHAPTER- 2: BASIC CONCEPT'S. BY: AHMED SAKR. SUPERVISED BY: PROF. HESHAM HAMED, DR. MAHMOUD A. ABDELGHANY.
- 2. Introduction RF section of Cellphone RF section of a cellphone
- 3. Introduction Design bottleneck RF Section is the bottleneck of wireless communication systems. Because: - The performance of the RF front end affects the overall performance of the entire system. - RF design involves many disciplines the designer should understand. - There are many trade-offs in RF design. - Relay on experience even while using design tools. Trade-offs in RF design
- 4. Basic concepts. Design bottleneck Nonlinearity • Harmonic distortion. • Compression. • Intermodulation. • Dynamic nonlinear systems. Noise • Noise Spectrum. • Device Noise. • Noise in circuits. Impedance Transformation • Series- Parallel conversion. • Matching networks. • S-Parameters.
- 5. Unites in RF Logarithmic operations review 𝑖𝑓 10 𝐴 = 𝐵 , 𝑡ℎ𝑒𝑛 log 𝐵 = 𝐴 log 1 𝑥 = − log 𝑥 log 10 𝑥 = 𝑥 log 𝑥 𝑎 = 𝑎𝑙𝑜𝑔(𝑥) log 𝑥𝑦 = log 𝑥 + log 𝑦 log 𝑥 𝑦 = log 𝑥 − log 𝑦
- 6. Unites in RF Gain Rin Rout Vin Vout 𝑽𝒐𝒍𝒕𝒂𝒈𝒆 𝒈𝒂𝒊𝒏 𝑨 𝒗 = 𝑉𝑜𝑢𝑡 𝑉𝑖𝑛 𝑅𝑀𝑆 𝑷𝒐𝒘𝒆𝒓 𝒈𝒂𝒊𝒏 𝑨 𝑷 = 𝑃𝑜𝑢𝑡 𝑃𝑖𝑛 = 𝑉𝑜𝑢𝑡2 𝑅𝑜𝑢𝑡 𝑉𝑖𝑛2 𝑅𝑖𝑛 = 𝑉𝑜𝑢𝑡2 𝑉𝑖𝑛2 × 𝑅𝑜𝑢𝑡 𝑅𝑖𝑛 = 𝐴𝑣2 × 𝑅𝑜𝑢𝑡 𝑅𝑖𝑛 𝐢𝐟 𝐑𝐨𝐮𝐭 = 𝐑𝐢𝐧 ⇒ 𝐀 𝐏 = 𝐀 𝐯 𝟐
- 7. Unites in RF Gain (in dB) 𝒅𝑩 𝑨 𝒗 = 20log( 𝑉𝑜𝑢𝑡 𝑉𝑖𝑛 ) 𝒅𝑩 𝑨 𝑷 = 10 log 𝑃𝑜𝑢𝑡 𝑃𝑖𝑛 = 10 log 𝑉𝑜𝑢𝑡2 𝑉𝑖𝑛2 × 𝑅𝑜𝑢𝑡 𝑅𝑖𝑛 𝑠𝑖𝑔𝑛𝑎𝑙 𝑝𝑜𝑤𝑒𝑟| 𝑑𝐵 𝑃𝑠 = 10 log 𝑃𝑠 1𝑚𝑊 → 𝑖𝑓 𝑅𝑜𝑢𝑡 = 𝑅𝑖𝑛 ⇒ 𝒅𝑩 𝑨 𝒑 = 𝒅𝑩(𝑨 𝒗) 𝑽𝒐𝒍𝒕𝒂𝒈𝒆 𝒈𝒂𝒊𝒏 𝑨 𝒗 = 𝑉𝑜𝑢𝑡 𝑉𝑖𝑛 𝑅𝑀𝑆 𝑷𝒐𝒘𝒆𝒓 𝒈𝒂𝒊𝒏 𝑨 𝑷 = 𝑃𝑜𝑢𝑡 𝑃𝑖𝑛 = 𝑉𝑜𝑢𝑡2 𝑅𝑜𝑢𝑡 𝑉𝑖𝑛2 𝑅𝑖𝑛 = 𝑉𝑜𝑢𝑡2 𝑉𝑖𝑛2 × 𝑅𝑜𝑢𝑡 𝑅𝑖𝑛 = 𝐴𝑣2 × 𝑅𝑜𝑢𝑡 𝑅𝑖𝑛 → 𝐢𝐟 𝐑𝐨𝐮𝐭 = 𝐑𝐢𝐧 ⇒ 𝐀 𝐏 = 𝐀 𝐯 𝟐
- 8. Unites in RF Voltage gain Vs. power gain Rin Rout Vin Vout We are interested in calculating the output voltage rather than the output power when the input and output impedance are not equal or contain negligible real parts. Why? Because the voltage gain is not equal to the power gain in this case, which is common in RF design.
- 9. Linearity and time variance Linearity For a linear system, if: X1(t) → Y1(t) , X2(t) → Y2(t) aX1(t) + bX2(t) → aY1(t) + bY2(t) Otherwise, the system is nonlinear. Time Variance For a time invariant system, if: X(t) → Y(t) Then : X(t-T)→ Y(t-T) Otherwise, the system is time variant. What about nonzero initial conditions and dc offsets? - They are linear too.
- 10. Linearity and time variance Switching system Nonlinear, time variant Linear, time variant
- 11. Linearity and time variance Nonlinear, time variant
- 12. Linearity and time variance Linear , time variant Vin2 delayed by 45 degree
- 13. Memory-less systems [outputs don’t depend on past values of input(s), opposite to Dynamic systems.] Memory-less linear systems y(t) = x(t) Memory-less nonlinear systems y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t) If j=0 for even j, the system is said to have odd symmetry, when his response to –x(t) is negative to that to x(t). The circuit having this property is called differential or balanced.
- 14. Nonlinearity effects. y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t) DC component Total Gain [compression @ 1 3 <0] 2nd harmonic Suppresse d for odd symmetry. 3rd harmonic Small signal gain
- 15. Harmonic distortion. y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t) DC component fundamental 2nd Harmonic 3rd Harmonic In many RF designs, the harmonics distortion is unimportant but should be tested before they are dismissed, usually harmonics are filtered, but it is a key parameter to test the performance of specific circuits such as Mixers Common in MIXERS &OSC
- 16. Gain compression y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t) DC component Total Gain [compression @ 1 3 <0] 2nd harmonic Suppresse d for odd symmetry. 3rd harmonic Small signal gain @ 1 3 <0 the gain is compressed as A rises 1 =500 3 =-0.1
- 17. Gain compression [1-dB compression point] @ 1-dB compression point, the gain is reduced by 10% Desensitization: when large interferer [blocker] causes gain compression while sensing weak desired signal. [lowers the SNR]
- 18. Cross modulation. y(t) = 1 x(t) + 2 x2(t) + 3 x3(t) +… n xn(t) Weak signal + large interferer large interferer: Variations in A2 (modulation) affects the amplitude of the signal (A1) Common in AMPLIFIERS
- 20. Intermodulation. Third order intermodulation products are the most important. If the difference between w1 and w2 is small they will appear close to the fundamentals, making it hard to design a filter to discard the effect of them. This effect is significant in LNA as shown in next figure…
- 21. Intermodulation[two-tone test]. Two signals with small A is chosen to minimize nonlinearity effect on it Gain = 1 Fundamental A IM products A3 Plot in log-log scale, the intersection is the third-order intercept point IIP3 is beyond the allowable input range or even higher than the supply voltage, because if the input level reached the AIP3 the gain drops and higher order IM products become significant.
- 22. Intermodulation[two-tone test]. IIP3 is chosen beyond the allowable input range or even higher than the supply voltage, because if the input level reached the AIP3 the gain drops and higher order IM products become significant. AIIP3 is greater than the 1-dB compression point with 9.6 dB
- 23. IIP3 direct calculation. [two-tone test].
- 24. Any Questions?