Lecture 9 RF Amplifier Design. Johan Wernehag, EIT. Johan Wernehag Electrical and Information Technology

Transcription

1 Lecture 9 RF Amplifier Design Johan Wernehag Electrical and Information Technology

2 Lecture 9 Oscillators Oscillators Based on Feedback Requirements for Self-Oscillation Output Power and Harmonic Distortion Tuned LC Oscillators Oscillator Noise Negative Resistance Oscillators Voltage Controlled Oscillators (VCO) Resonators Crystal Oscillators (XO) Some Good Practical Advice about Oscillator Design

3 Black s Feedback Model V out = A v V A V A = V in + bv out V in V A V out + A V β A f = V out V in = A v 1- A v b Barkhaussen oscillation criteria: A v b = 1 A v b is called the loop gain

4 Oscillators Based on Feedback If the oscillator runs at constant amplitude it complies with the Barkhaussen oscillation criteria: Feedback network b A v b = 1 i.e. A v b = 1 Amplifier and arg( A v b) = 0 A v A v = voltage gain β = feedback factor

5 Output Power and Harmonic Distortion P f0 P 2 f0 P 3 f0 A V β = 1 when the oscillator runs at constant amplitude = A v b = 1

6 The Generalized Oscillator Model for LC Oscillators The phase criteria in Barkhaussen is fulfilled when X 1 + X 2 + X 3 = 0 i.e. the circuit is at resonance A v X 3 X 1 R L X 2 The amplitude criteria in Barkhaussen is fulfilled when b = 1 A v = X 1 X 1 + X 3 = X 1 -X 2 = X 2 + X 3 X 2 Tip: choose an expression for β where both reactance's are inductive or capacitive

7 Oscillator Circuits The feedback network in LC oscillators may be configured in different ways: Hartley Colpitts Clapp v v one capacitive branch two inductive branches v v two capacitive branches one inductive branch v a variation of the Colpitts oscillator Depending on the selected transistor configuration (CE, CB or CC) there are a lot more variations.

8 Example 1 Oscillator Analysis large 1. determine the amplifier configuration (CE, CB or CC)? large 2. identify components that determines the frequency and feedback? 3. draw the generalized oscillator model Example 2 4. calculate the voltage gain A V 5. calculate the resonant frequency f 0 6. calculate the feedback factor β 7. check if the Barkhaussen criteria is fulfilled large

9 Calculation of A V and β A v b = 1 A v = g m R ctot g m = I C V T R ctot = R p / /R L / / R in / /r o R p =Q u w 0 L æ R in = (( r e //R 3 )+R 4 ) ç è C 3 +C 4 C 3 ö ø 2 compare with lab 4! b = ( r e //R 3 ) ( r e //R 3 )+R 4 C 3 C 3 +C 4

10 Oscillator Noise The noise level increases close to the resonant frequency as A A f g when f g f 0 A f = 1- ba

11 Noise Model of the Oscillator N i = FkT 0 [ W/Hz] N + 0 = G f FkT 0 W/Hz A [ ] b( f ) A f A ( f )= 1-b( f)a G 2 f = A f b( f)= b 0 1+ jq 2 f - f 0 f 0

12 N 0 é W ù ë ê Hz û ú N 02 Noise Spectrum N 02 = GFkT æ 2 0 f 0 4Q 2 ç è d f 2 + a 2 ( ) ö W/Hz ø [ ] 6 db/octave N 01 = GFkT 0 [ W/Hz] N 01 a = FGkT 0p f 0 2 4P osc Q 2 f b = f 0 2Q To achieve low phase noise choose: a high-q resonant circuit a low noise amplifier as low gain as possible high power level in the oscillator The noise consists of both amplitude and phase noise if a limiter is used the amplitude noise will be suppressed and the total noise level is reduced by 3 db d f = f - f 0 [ Hz]

13 Negative Resistance Oscillators Lab 4 Which transistor configuration is used? A serial inductor (a short-circuited stub) is inserted to the base to intentionally make the transistor unstable A resonator (an open stub) is connected to the input to set the resonant frequency

14 Negative Resistance Oscillator Lab 4 stub e b c V CC out

15 Conditions for Oscillation in a Two-Port K = 1+D S 11 - S 22 < 1 2 S 12 S 21 D = S 11 S 22 - S 21 S 12 G IN G S = 1 G UT G L = 1 Express this in impedance! G IN G S = R IN + jx IN - Z 0 R IN + jx IN + Z 0 R S + jx S - Z 0 R S + jx S + Z 0 = 1 R IN + R S = 0 X IN + X S = 0

16 Voltage Controlled Oscillator (VCO) Clapp oscillator f out VCC L Vcontrol C3 Cvar C1 C2 OUT V control GND Negative resistance oscillator Varicap diode C var V control

17 Varicap Diode Forward bias Reversed bias Ex.: BB811 P N P N C d ( V R )= ( ) C j 0 æ 1+ V ö R ç è V j ø M V R = reverse voltage

18 Resonators In order to improve the Q-factor, instead of or as a compliment to the LC circuit, you may use: Transmission line microstrip resonator coaxial resonator Ceramic resonator Quartz crystal

19 The Quartz Crystal (Xtal) equivalent circuit diagram Symbol r L Cp L = 5 mh C p» 10 pf C s» 50 ff r < 3 W Cs Q» 10 5

20 The Impedance of a Crystal = R + jx Z Z rq ( 2 +1) Series resonant frequency Parallel resonant frequency r X f s f p X f f s f p f X -

21 Crystal Oscillators circuit examples series resonance parallel resonance parallel resonance

22 Pierce Crystal Oscillator Compare with lab 4!

23 Some Good Practical Advice about Oscillator Design Generally: select components of high quality use buffer amplifier use filtered and well stabilized supply voltage apply good shielding For high frequency stability: design the resonant circuit for high Q use a ceramic resonator alternatively a quartz crystal pre-aging of crystals the oscillator may be enclosed in a temperature controlled oven frequency control by temperature sensor and varicap diode Low phase noise: design the resonant circuit for high Q use low noise amplifier use as low gain as possible let the oscillator operate at a high power level