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**RF Electronics Engineering**

Spring 2014 RF Systems and Circuits RF Electronics Engineering Emad Hegazi Professor, ECE Communication Circuits Research Group

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Spring 2014 RF Systems and Circuits Resonance Resonance represents the intrinsic rate of energy exchange in a second order system. Friction forces oscillation to cease after a while. Less friction means higher quality system

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**Circuit Analysis RF Systems and Circuits Why? If there is no loss**

Spring 2014 RF Systems and Circuits Circuit Analysis If there is no loss Why? define

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Spring 2014 RF Systems and Circuits Resonance Inductor and Capacitor exchange energy and loss resistance keeps burning energy By the way, the parallel resistance is simply a model.

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**Susceptance @ Resonance**

Spring 2014 RF Systems and Circuits Resonance R is the ONLY block that draws current from the source at resonance The tank looks like a high impedance to the supply.

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**Quality The ratio of stored current to the source current at resonance**

Spring 2014 RF Systems and Circuits Quality The ratio of stored current to the source current at resonance R must be large for higher Q.

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Spring 2014 RF Systems and Circuits Series Resonance

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**Getting Real RF Systems and Circuits If the input source is constant**

Spring 2014 RF Systems and Circuits Getting Real If the input source is constant

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Spring 2014 RF Systems and Circuits Resonance Inductor and Capacitor exchange energy and loss resistance keeps burning energy The impedance is at minimum when at resonance

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Spring 2014 RF Systems and Circuits Resonance Q is the ratio between the voltage on the reactance to the source voltage.

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**Passive Amplification**

Spring 2014 RF Systems and Circuits Passive Amplification QVm -QVm Maximum current flows in the circuit means L & C see maximum voltage at opposite polarities. @ resonance, the circuit amplifies the source voltage by Q

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Spring 2014 RF Systems and Circuits Impedance Conversion

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Spring 2014 RF Systems and Circuits Impedance Conversion

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**Outline Friis Formula Merits of LNAs Common Gate LNA Common Source LNA**

Spring 2014 RF Systems and Circuits Outline Friis Formula Merits of LNAs Common Gate LNA Common Source LNA

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Spring 2014 RF Systems and Circuits Cascaded Noise Figure In a line-up of receiver stages, use Friis equation Gi is the power gain Says that the noise factor ‘F’ is more influenced by earlier stages

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**LNA Merits Gain Low Noise (NF) High Linearity (IIP3)**

Spring 2014 RF Systems and Circuits LNA Merits Gain Low Noise (NF) High Linearity (IIP3) Low Reflection (S11) High reverse isolation (S12) High Stability (K)

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**Maximum Power Transfer**

Spring 2014 RF Systems and Circuits Maximum Power Transfer

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**Transistor Noise Thermal noise is referred to the input**

Spring 2014 RF Systems and Circuits Transistor Noise Thermal noise is referred to the input Physical Circuit equivalent

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**Common Gate LNA Input impedance is resistive (except for parasitics)**

Spring 2014 RF Systems and Circuits Common Gate LNA Input impedance is resistive (except for parasitics) Offers good impedance match even at low frequencies

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Spring 2014 RF Systems and Circuits Common Gate LNA tunes out transistor and board parasitics. Channel resistance offers good reverse isolation

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**Common Gate LNA At matching condition, Zin = 1/gm**

Spring 2014 RF Systems and Circuits Common Gate LNA At matching condition, Zin = 1/gm

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**Impedance Transformers**

Spring 2014 RF Systems and Circuits Impedance Transformers

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**Impedance Matching Maximum power transfer Minimum noise figure**

Spring 2014 RF Systems and Circuits Impedance Matching Maximum power transfer Minimum noise figure Optimized passives’ transfer functions Minimum reflections

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**Impedance Matching Impedance mismatch is preserved at each port**

Spring 2014 RF Systems and Circuits Impedance Matching Impedance mismatch is preserved at each port We need a TRANSFORMER

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**Transformer Matching Transformers are bulky and lossy**

Spring 2014 RF Systems and Circuits Transformer Matching Transformers are bulky and lossy We don’t really need wideband matching in RF transceivers Think of a narrow band equivalent of a transformer

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**Narrow Band Impedance Transformers**

Spring 2014 RF Systems and Circuits Narrow Band Impedance Transformers Load resistance takes only a fraction of the input current Looks like a higher resistance than it really is. Problem: Zin looks reactive

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**L-Match @resonance the C and Ls tune out and only Rs remains.**

Spring 2014 RF Systems and Circuits L-Match @resonance the C and Ls tune out and only Rs remains. LNA input is made with higher R to save power LNA Antenna

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**Common Gate LNA: Lowering Power II**

Spring 2014 RF Systems and Circuits Common Gate LNA: Lowering Power II Narrowband impedance transformer (L Section) allows the LNA to have Zin>50W. Transformer amplifies input signal by:

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**Common Gate LNA: Lowering Power II**

Spring 2014 RF Systems and Circuits Common Gate LNA: Lowering Power II For same IIP3, Veff has to increase by >1 Current is reduced by the same factor Bias current is given by: gm

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**Common Gate LNA: Lowering Power III**

Spring 2014 RF Systems and Circuits Common Gate LNA: Lowering Power III gm

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Input impedance is purely capacitive Resistive part appears at high frequency No input matching is possible

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Rg is set to 50W => Input Matching Miller Effect due to Cgd => Limited Bandwidth

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Cascode reduces Miller Effect Resistive Load limits linearity

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Parallel Resonance at output boasts narrow band gain without impacting linearity Rg produces a lot of Noise NF>3 dB

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Series resonance at input creates a resistive term Iin= jw CgsVgs Vin=Vgs+jwLs(Iin+gmVgs) gmVgs Iin

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Series resonance at input creates a resistive term @ RF, input is still capacitive because Ls is very small to give 50W with high wT

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Gate inductance offers one more degree of freedom to allow matching and series resonance at the same time Valid for

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Spring 2014 RF Systems and Circuits Parasitics Ali Niknejad ECE142

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**Design Procedure for Common Source LNAs**

Spring 2014 RF Systems and Circuits Design Procedure for Common Source LNAs

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Assume an equivalent resistive load Rd @ resonance

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**Common Source Amplifier**

Spring 2014 RF Systems and Circuits Common Source Amplifier Noise Figure (F) is given by Source Coils Transistor Use samll Ls Decreases with wT

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**Optimization of CS LNA Assume @ Input matching condition**

Spring 2014 RF Systems and Circuits Optimization of CS LNA Assume @ Input matching condition

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**Optimization of CS LNA wT Increases Lg Noise dominates Higher power**

Spring 2014 RF Systems and Circuits Optimization of CS LNA wT Increases Lg Noise dominates Higher power

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**Another Way to Look at It**

Spring 2014 RF Systems and Circuits Another Way to Look at It If Q is input quality factor

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**Another Way to Look at It**

Spring 2014 RF Systems and Circuits Another Way to Look at It The input is amplified by Q before it reaches the transistor This reduces linearity

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**Other Losses: Inductor Losses**

Spring 2014 RF Systems and Circuits Other Losses: Inductor Losses Typically Lg losses dominate Adds in series to source noise Independent of FET gain

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**Other Losses: Gate Resistance**

Spring 2014 RF Systems and Circuits Other Losses: Gate Resistance Gate Resistance creates additional noise (uncorrelated with channel noise) Use inter-digitated layout to reduce gate electrode resistance

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**Other Losses: Gate Induced Noise**

Spring 2014 RF Systems and Circuits Other Losses: Gate Induced Noise Due to inversion layer resistance Partly correlated with conventional thermal noise Modeled as a resistance in series with gate

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**Other Losses: Gate Induced Noise**

Spring 2014 RF Systems and Circuits Other Losses: Gate Induced Noise The effective Q is lowered by losses Higher Q is achieved through lower Cgs Smaller Cgs raises rinv and also gate resistance There is an optimum W at each current

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**Other Losses: Substrate Coupling**

Spring 2014 RF Systems and Circuits Other Losses: Substrate Coupling BSIM3V3 models do NOT capture Cgb Gate to bulk capacitance is an additional path for noise

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**Other Losses: Substrate Coupling**

Spring 2014 RF Systems and Circuits Other Losses: Substrate Coupling Hole distribution in the depletion layer are modulated by gate voltage Same effect on electrons in the inversion layer which reflects back on depletion region

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