Lesson 10-RF Oscillators

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Agenda: Positive feedback oscillator concepts, negative resistance oscillator concepts (typically employed for RFoscillator), equivalence between positive feedback and negative resistance oscillator theory, oscillator start-up requirement and transient, oscillator design - Making an amplifier circuit unstable, constant |Γ1| circle, fixed frequency oscillator design, voltage-controlled oscillator design. 10 - RF Oscillators The information in this work has been obtained from sources believed to be reliable The author does not guarantee the accuracy or completeness of any information presented herein, and shall not be responsible for any errors, omissions or damages as a result of the use of this information April 2012  2006 by Fabian Kung Wai Lee Main References • • • • • • • • [1]* D.M Pozar, “Microwave engineering”, 2nd Edition, 1998 John-Wiley & Sons [2] J Millman, C C Halkias, “Integrated electronics”, 1972, McGraw-Hill [3] R Ludwig, P Bretchko, “RF circuit design - theory and applications”, 2000 Prentice-Hall [4] B Razavi, “RF microelectronics”, 1998 Prentice-Hall, TK6560 [5] J R Smith,”Modern communication circuits”,1998 McGraw-Hill [6] P H Young, “Electronics communication techniques”, 5th edition, 2004 Prentice-Hall [7] Gilmore R., Besser L.,”Practical RF circuit design for modern wireless systems”, Vol & 2, 2003, Artech House [8] Ogata K., “Modern control engineering”, 4th edition, 2005, Prentice-Hall April 2012  2006 by Fabian Kung Wai Lee Agenda • • • • • • • • Positive feedback oscillator concepts Negative resistance oscillator concepts (typically employed for RF oscillator) Equivalence between positive feedback and negative resistance oscillator theory Oscillator start-up requirement and transient Oscillator design - Making an amplifier circuit unstable Constant |Γ1| circle Fixed frequency oscillator design Voltage-controlled oscillator design April 2012  2006 by Fabian Kung Wai Lee 1.0 Oscillation Concepts April 2012  2006 by Fabian Kung Wai Lee Introduction • • • • • • Oscillators are a class of circuits with terminal or port, which produce a periodic electrical output upon power up Most of us would have encountered oscillator circuits while studying for our basic electronics classes Oscillators can be classified into two types: (A) Relaxation and (B) Harmonic oscillators Relaxation oscillators (also called astable multivibrator), is a class of circuits with two unstable states The circuit switches back-and-forth between these states The output is generally square waves Harmonic oscillators are capable of producing near sinusoidal output, and is based on positive feedback approach Here we will focus on Harmonic Oscillators for RF systems Harmonic oscillators are used as this class of circuits are capable of producing stable sinusoidal waveform with low phase noise April 2012  2006 by Fabian Kung Wai Lee 2.0 Overview of Feedback Oscillators April 2012  2006 by Fabian Kung Wai Lee Classical Positive Feedback Perspective on Oscillator (1) • • Consider the classical feedback system with non-inverting amplifier, Assuming the feedback network and amplifier not load each other, we can write the closed-loop transfer function as: Non-inverting amplifier Si(s) E(s) + So(s) A(s) + High impedance Positive Feedback • • Feedback network High impedance F(s) So (s ) = 1− AA(s(s)F) (s ) (2.1a) Si T (s ) = A(s )F (s ) (2.1b) Loop gain (the gain of the system around the feedback loop) Writing (2.1a) as: S o (s ) = 1− AA(s()sF) (s ) S i (s ) We see that we could get non-zero output at So, with Si = 0, provided 1-A(s)F(s) = Thus the system oscillates! April 2012  2006 by Fabian Kung Wai Lee Classical Positive Feedback Perspective on Oscillator (1) • The condition for sustained oscillation, and for oscillation to startup from positive feedback perspective can be summarized as: For sustained oscillation For oscillation to startup • • − A(s )F (s ) = A(s )F (s ) > Barkhausen Criterion arg( A(s )F (s )) = (2.2a) (2.2b) Take note that the oscillator is a non-linear circuit, initially upon power up, the condition of (2.2b) will prevail As the magnitudes of voltages and currents in the circuit increase, the amplifier in the oscillator begins to saturate, reducing the gain, until the loop gain A(s)F(s) becomes one A steady-state condition is reached when A(s)F(s) = Note that this is a very simplistic view of oscillators In reality oscillators are non-linear systems The steady-state oscillatory condition corresponds to what is called a Limit Cycle See texts on non-linear dynamical systems April 2012  2006 by Fabian Kung Wai Lee Classical Positive Feedback Perspective on Oscillator (2) • Positive feedback system can also be achieved with inverting amplifier: Inverting amplifier Si(s) E(s) + -A(s) So(s) - So (s ) = 1− AA(s(s)F) (s ) Si Inversion F(s) • • To prevent multiple simultaneous oscillation, the Barkhausen criterion (2.2a) should only be fulfilled at one frequency Usually the amplifier A is wideband, and it is the function of the feedback network F(s) to ‘select’ the oscillation frequency, thus the feedback network is usually made of reactive components, such as inductors and capacitors April 2012  2006 by Fabian Kung Wai Lee Classical Positive Feedback Perspective on Oscillator (3) • • In general the feedback network F(s) can be implemented as a Pi or T network, in the form of a transformer, or a hybrid of these Consider the Pi network with all reactive elements A simple analysis in [2] and [3] shows that to fulfill (2.2a), the reactance X1, X2 and X3 need to meet the following condition: So(s) E(s) + -A(s) X = −( X + X ) (2.3) - If X3 represents inductor, then X1 and X2 should be capacitors X3 X1 April 2012 X2  2006 by Fabian Kung Wai Lee 10 Classical Feedback Oscillators • The following are examples of oscillators, based on the original circuit using vacuum tubes + + + - - - Colpitt oscillator + Hartley oscillator - Armstrong oscillator Clapp oscillator April 2012  2006 by Fabian Kung Wai Lee 11 Example of Tuned Feedback Oscillator (1) A 48 MHz Transistor Common -Emitter Colpitt Oscillator 2.0 1.5 1.0 R RB1 R=10 kOhm R RC R=330 Ohm C CD1 C=0.1 uF VB VL C Cc2 C=0.01 uF pb_mot_2N3904_19921211 Q1 R RB2 R=10 kOhm 0.5 0.0 -0.5 VC C Cc1 C=0.01 uF VB, V VL, V V_DC SRC1 Vdc=3.3 V R RE R=220 Ohm -1.0 R RL R=220 Ohm -1.5 A(ω )F (ω ) C CE C=0.01 uF 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 time, usec Si(s) L C L1 C1 L=2.2 uH C=22.0 pF R= C C2 C=22.0 pF t E(s) + -A(s) So(s) - F(s) April 2012  2006 by Fabian Kung Wai Lee 12 Example of Tuned Feedback Oscillator (2) A 27 MHz Transistor Common-Base Colpitt Oscilator 600 R RC R=470 Ohm R RB1 R=10 kOhm VC R RE R=100 Ohm -400 L L1 L=1.0 uH R= C C2 C=100.0 pF C C3 C=4.7 pF R R1 R=1000 Ohm -600 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 time, usec E(s) + -200 pb_m ot_2N3904_19921211 Q1 VE R RB2 R=4.7 kOhm Si(s) 200 VL C C1 C=100.0 pF C Cc2 C=0.1 uF VB C Cc1 C=0.1 uF 400 C CD1 C=0.1 uF VE, mV VL, mV V_DC SRC1 Vdc=3.3 V So(s) A(s) + F(s) April 2012  2006 by Fabian Kung Wai Lee 13 Example of Tuned Feedback Oscillator (3) V_DC SRC1 Vdc=3.3 V R RB1 R=10 kOhm R RC R=330 Ohm A 16 MHz Transistor Common-Emitter Crystal Oscillator C CD1 C=0.1 uF VC VB C Cc1 C=0.1 uF C C1 C=22.0 pF April 2012 VL C Cc2 C=0.1 uF R RL R=220 Ohm pb_mot_2N3904_19921211 Q1 R RB2 R=10 kOhm R RE R=220 Ohm C CE C=0.1 uF sx_stk_CX-1HG-SM_A_19930601 XTL1 Fres=16 MHz C C2 C=22.0 pF  2006 by Fabian Kung Wai Lee 14 Limitation of Feedback Oscillator • • • • At high frequency, the assumption that the amplifier and feedback network not load each other is not valid In general the amplifier’s input impedance decreases with frequency, and it’s output impedance is not zero Thus the actual loop gain is not A(s)F(s) and equation (2.2) breakdowns Determining the loop gain of the feedback oscillator is cumbersome at high frequency Moreover there could be multiple feedback paths due to parasitic inductance and capacitance It can be difficult to distinguish between the amplifier and the feedback paths, owing to the coupling between components and conductive structures on the printed circuit board (PCB) or substrate Generally it is difficult to physically implement a feedback oscillator once the operating frequency is higher than 500MHz April 2012  2006 by Fabian Kung Wai Lee 15 3.0 Negative Resistance Oscillators April 2012  2006 by Fabian Kung Wai Lee 16 Introduction (1) • • • • • • • An alternative approach is needed to get a circuit to oscillate reliably We can view an oscillator as an amplifier that produces an output when there is no input Thus it is an unstable amplifier that becomes an oscillator! For example let’s consider a conditionally stable amplifier Here instead of choosing load or source impedance in the stable regions of the Smith Chart, we purposely choose the load or source impedance in the unstable impedance regions This will result in either |Γ1 | > or |Γ2 | > The resulting amplifier circuit will be called the Destabilized Amplifier As seen in Chapter 7, having a reflection coefficient magnitude for Γ1 or Γ2 greater than one implies the corresponding port resistance R1 or R2 is negative, hence the name for this type of oscillator April 2012  2006 by Fabian Kung Wai Lee 17 Introduction (2) • • • For instance by choosing the load impedance ZL at the unstable region, we could ensure that |Γ1 | > We then choose the source impedance properly so that |Γ1 Γs | > and oscillation will start up (refer back to Chapter on stability theory) Once oscillation starts, an oscillating voltage will appear at both the input and output ports of a 2-port network So it does not matter whether we enforce |Γ1 Γs | > or |Γ2 ΓL | > 1, enforcing either one will cause oscillation to occur (It can be shown later that when |Γ1 Γs | > at the input port, |Γ2 ΓL | > at the output port and vice versa) The key to fixed frequency oscillator design is ensuring that the criteria |Γ1 Γs | > only happens at one frequency (or a range of intended frequencies), so that no simultaneous oscillations occur at other frequencies April 2012  2006 by Fabian Kung Wai Lee 18 Recap - Wave Propagation Stability Perspective (1) • From our discussion of stability from wave propagation in Chapter 7… Zs or Γs Source b1 bsΓs 2Γ13 bsΓs 3Γ14 April 2012 Port 2-port Network a1 Z1 or Γ1 bsΓ1 bsΓs Γ12 Port a1 = bs + bs Γ1Γs + bs Γ12Γs + bs ⇒ a1 = − Γ1Γs b1 = bs Γ1 + bs Γ12Γs + bs Γ13Γs + ⇒ b1 = bs bsΓs Γ1 b ⇒ 1= bs Γ1 − Γ1Γs Compare with equation (2.1a) bsΓs 2Γ12 bsΓs 3Γ13 bs Γ1 − Γ1Γs So A(s ) ( s) = Si 1− A(s )F (s ) Similar mathematical form  2006 by Fabian Kung Wai Lee 19 Recap - Wave Propagation Stability Perspective (2) • • • • We see that the infinite series that constitute the steady-state incident (a1) and reflected (b1) waves at Port will only converge provided |Γ sΓ1| < These sinusoidal waves correspond to the voltage and current at the Port If the waves are unbounded it means the corresponding sinusoidal voltage and current at the Port will grow larger as time progresses, indicating oscillation start-up condition Therefore oscillation will occur when |Γ sΓ1 | > Similar argument can be applied to port since the signals at Port and are related to each other in a two-port network, and we see that the condition for oscillation at Port is |ΓLΓ2 | > April 2012  2006 by Fabian Kung Wai Lee 20 10 Schematic of the VCO Initial noise source to start the oscillation t VtP WL Vtrig V_Tran=pwl(t ime, 0ns , 0V, 1ns,0 01V, 2ns ,0V) R Rb R=47 k Ohm V_DC Vcc Vdc =3.0 V Variable capacitance tuning network R V _D C R1 R=4700 Ohm S RC1 V dc=-1.5 V Tran Tran1 StopTim e=100 ns ec MaxTimeS tep=1.2 nsec L Lc L=220.0 nH R= P ARAM ET ER SWEEP ParamSweep Sweep1 SweepVar="R load" SimI ns tanc eNam e[1] ="Tran1" SimI ns tanc eNam e[2] = SimI ns tanc eNam e[3] = SimI ns tanc eNam e[4] = SimI ns tanc eNam e[5] = SimI ns tanc eNam e[6] = St art=100 St op=700 V ar VAR E qn St ep=100 VAR X=1 R load=100 R C Rout C c2 C =330 pF R=50 O hm L L2 L=47 nH R= C Cb1 C=2 pF C Cb3 C=4 pF C Cb2 C=10 pF April 2012 T R ANS IE NT DC DC D C1 pb_phl_BF R92A_19921214 Q1 R RL R=Rload R Re R=220 O hm di_s ms _bas 40_19930908 D1 C 2-port network C b4 C =4.7 pF  2006 by Fabian Kung Wai Lee 69 More on the Schematic • • • • L2 together with Cb3, Cb4 and the junction capacitance of D1 can produce a range of reactance value, from negative to positive Together these components form the frequency determining network Cb4 is optional, it is used to introduce a capacitive offset to the junction capacitance of D1 R1 is used to isolate the control voltage Vdc from the frequency determining network It must be a high quality SMD resistor The effectiveness of isolation can be improved by adding a RF choke in series with R1 and a shunt capacitor at the control voltage Notice that the frequency determining network has no actual resistance to counter the effect of |R1(ω)| This is provided by the loss resistance of L2 and the junction resistance of D1 April 2012  2006 by Fabian Kung Wai Lee 70 35 Time Domain Result 1.0 0.5 0.0 -0.5 -1.0 -1.5 10 20 30 40 50 60 70 80 90 100 Vout when Vdc = -1.5V April 2012  2006 by Fabian Kung Wai Lee 71 Load-Pull Experiment • Peak-to-peak output voltage versus Rload for Vdc = -1.5V Vout(pp) 100 200 300 400 500 600 700 800 RLoad April 2012  2006 by Fabian Kung Wai Lee 72 36 Controlling Harmonic Distortion (1) • Since the resistance in the frequency determining network is too small, large amount of non-linearity is needed to limit the output voltage waveform, as shown below there is a lot of distortion Vout April 2012  2006 by Fabian Kung Wai Lee 73 Controlling Harmonic Distortion (2) • • The distortion generates substantial amount of higher harmonics This can be reduced by decreasing the positive feedback, by adding a small capacitance across the collector and base of transistor Q1 This is shown in the next slide April 2012  2006 by Fabian Kung Wai Lee 74 37 Controlling Harmonic Distortion (3) The observant person would probably notice that we can also reduce the harmonic distortion by introducing a series resistance in the tuning network However this is not advisable as the phase noise at the oscillator’s output will increase ( more about this later) Control voltage Vcontrol April 2012 Capacitor to control positive feedback DC DC DC1 t TRANSIENT Tran Tran1 StopTime=280.0 nsec MaxTimeStep=1.2 nsec VtPWL L Vtrig Lc V_Tran=pwl(time, 0ns, 0V, 1ns,0.01V, 2ns,0V) L=220.0 nH R R= Rb R=47 kOhm I_Probe V_DC I_Probe Iload Vcc IC Vdc=3.0 V C Ccb C=1.0 pF L L2 L=47.0 nH C R= Cb1 pb_phl_BFR92A_19921214 C=6.8 pF Q1 C Cb3 C=4.7 pF C Cb2 C=10.0 pF R R1 V_DC R=4700 Ohm SRC1 Vdc=0.5 V C Cc2 C=330.0 pF R Rout R=50 Ohm R RL R=50 Ohm R Re R=220 Ohm di_sms_bas40_19930908 D1 C Cb4 C=0.7 pF  2006 by Fabian Kung Wai Lee 75 Controlling Harmonic Distortion (4) • The output waveform Vout after this modification is shown below: Vout April 2012  2006 by Fabian Kung Wai Lee 76 38 Controlling Harmonic Distortion (5) • • • Finally, it should be noted that we should also add a low-pass filter (LPF) at the output of the oscillator to suppress the higher harmonic components Such LPF is usually called Harmonic Filter Since the oscillator is operating in nonlinear mode, care must be taken in designing the LPF Another practical design example will illustrate this approach April 2012  2006 by Fabian Kung Wai Lee 77 The Tuning Range • Actual measurement is carried out, with the frequency measured using a high bandwidth digital storage oscilloscope 410 D1 is BB149A, a varactor manufactured by Phillips Semiconductor (Now NXP) 405 f MHz 400 395 0.5 1.5 2.5 Vdc April 2012  2006 by Fabian Kung Wai Lee Volts 78 39 Phase Noise in Oscillator (1) • • • Since the oscillator output is periodic In frequency domain we would expect a series of harmonics In a practical oscillation system, the instantaneous frequency and magnitude of oscillation are not constant These will fluctuate as a function of time vosc (t ) = (Vo + mnoise (t )) cos(ωt + θ + θ noise (t )) These random fluctuations are noise, and in frequency domain the effect of the spectra will ‘smear out’ t Ideal oscillator output fo 2fo f 3fo Smearing t Real oscillator output April 2012  2006 by Fabian Kung Wai Lee fo 2fo 3fo 79 f Phase Noise in Oscillator (2) • • Mathematically, we can say that the instantaneous frequency and magnitude of oscillation are not constant These will fluctuate as a function of time As a result, the output in the frequency domain is ‘smeared’ out v(t) T = 1/fo [ Leeson’s expression LPM ∝ 10 log FkT A ⋅ 8Q1 L ⋅ ( )] fo f offset t fo v(t) Large phase noise f Contains both phase and amplitude modulation of the sinusoidal waveform at frequency fo t f fo Small phase noise April 2012  2006 by Fabian Kung Wai Lee 80 40 Phase Noise in Oscillator (3) • Typically the magnitude fluctuation is small (or can be minimized) due to the oscillator nonlinear limiting process under steady-state • Thus the smearing is largely attributed to phase variation and is known as Phase Noise • Phase noise is measured with respect to the signal level at various offset frequencies Signal level vosc (t ) ≅ Vo cos(ωt + θ + θ noise (t )) • Phase noise is measured in dBc/Hz @ foffset • dBc/Hz stands for dB down from the carrier (the ‘c’) in Hz bandwidth • For example -90dBc/Hz @ 100kHz offset from a CW sine wave at 2.4GHz v(t) - 90dBc/Hz t 100kHz f fo Assume amplitude limiting effect Of the oscillator reduces amplitude fluctuation April 2012  2006 by Fabian Kung Wai Lee 81 Reducing Phase Noise (1) • Requirement 1: The resonator network of an oscillator must have a high Q factor This is an indication of low dissipation loss in the tuning network (See Chapter 3a – impedance transformation network on Q factor) Xtune X1 Tuning Network with High Q Variation in Xtune due to environment causes small change in instantaneous frequency Xtune X1 ∆f ∆f f -X1 April 2012 2∆|X1| Tuning Network with Low Q f -X1 Ztune = Rtune +jXtune  2006 by Fabian Kung Wai Lee 2∆|X1| 82 41 Reducing Phase Noise (2) • • • • • A Q factor in the tuning network of at least 20 is needed for medium performance oscillator circuits at UHF For highly stable oscillator, Q factor of the tuning network must be in excess or 1000 We have looked at LC tuning networks, which can give Q factor of up to 40 Ceramic resonator can provide Q factor greater than 500, while piezoelectric crystal can provide Q factor > 10000 At microwave frequency, the LC tuning networks can be substituted with transmission line sections See R W Rhea, “Oscillator design & computer simulation”, 2nd edition 1995, McGraw-Hill, or the book by R.E Collin for more discussions on Q factor Requirement 2: The power supply to the oscillator circuit should also be very stable to prevent unwanted amplitude modulation at the oscillator’s output April 2012  2006 by Fabian Kung Wai Lee 83 Reducing Phase Noise (3) • • • Requirement 3: The voltage level of Vcontrol should be stable Requirement 4: The circuit has to be properly shielded from electromagnetic interference from other modules Requirement 5: Use low noise components in the construction of the oscillator, e.g small resistance values, low-loss capacitors and inductors, low-loss PCB dielectric, use discrete components instead of integrated circuits April 2012  2006 by Fabian Kung Wai Lee 84 42 Example of Phase Noise from VCOs • Comparison of two VCO outputs on a spectrum analyzer* VCO output with high phase noise April 2012 VCO output with low phase noise  2006 by Fabian Kung Wai Lee *The spectrum analyzer internal oscillator must of course has a phase noise of an order of magnitude lower than our VCO under test 85 More Materials • • This short discussion cannot justice to the material on phase noise For instance the mathematical model of phase noise in oscillator and the famous Leeson’s equation is not shown here You can find further discussion in [4], and some material for further readings on this topic: – D Schere, “The art of phase noise measurement”, Hewlett Packard RF & Microwave Measurement Symposium, 1985 – T Lee, A Hajimiri, “The design of low noise oscillators”, Kluwer, 1999 April 2012  2006 by Fabian Kung Wai Lee 86 43 More on Varactor • • The varactor diode is basically a PN junction optimized for its linear junction capacitance It is always operated in the reverse-biased mode to prevent nonlinearity, which generate harmonics Vj • As we increase the negative biasing voltage Vj , Cj decreases, hence the oscillation frequency increases Cj • The abrupt junction varactor has high Q, but low sensitivity (e.g Cj varies little over large voltage change) • The hyperabrupt junction varactor Cjo Forward biased has low Q, but higher sensitivity Reverse biased Linear region April 2012 Vj  2006 by Fabian Kung Wai Lee 87 A Better Variable Capacitor Network • • • • The back-to-back varactors are commonly employed in a VCO circuit, so that at low Vcontrol, when one of the diode is being affected by the AC voltage, the other is still being reverse biased When a diode is forward biased, the PN junction capacitance becomes nonlinear The reverse biased diode has smaller junction capacitance, and this dominates the overall capacitance of the back-to-back varactor network This configuration helps to decrease the harmonic distortion To negative resistance amplifier At any one time, at least one of the diode will be reverse biased The junction capacitance of the reverse biased diode will dominate the overall capacitance of the network Sep 2013 To suppress RF signals Vcontrol  2006 by Fabian Kung Wai Lee Vcontrol To suppress RF signals + + Vcontrol Symbol for Varactor 88 44 Example 5.1 – VCO Design for Frequency Synthesizer • • • To design a low power VCO that works from 810 MHz to 910 MHz Power supply = 3.0V Output power (into 50Ω load) minimum -3.0 dBm April 2012  2006 by Fabian Kung Wai Lee 89 Example 5.1 Cont… • Checking the d.c biasing and AC simulation DC DC DC1 V_DC SRC1 Vdc=3.3 V R RB R=33 kOhm S-PARAMETERS S_Param SP1 Start=0.7 GHz Stop=1.0 GHz Step=1.0 MHz b82496c3120j000 LC param=SIMID 0603-C (12 nH +-5%) 100pF_NPO_0603 Cc2 pb_phl_BFR92A_19921214 Q1 4_7pF_NPO_0603 Term Cc1 Term1 Num=1 Z=50 Ohm Z11 April 2012 2_2pF_NPO_0603 C1 R RL R=100 Ohm 3_3pF_NPO_0603 C2 R RE R=100 Ohm  2006 by Fabian Kung Wai Lee 90 45 Example 5.1 Cont… • Checking the results – real and imaginary portion of Z1 when output is terminated with ZL = 100Ω m1 freq=775.0MHz m1=-89.579 m2 freq=809.0MHz m2=-84.412 -40 -50 imag(Z(1,1)) real(Z(1,1)) -60 -70 m2 -80 m1 -90 -100 -110 -120 0.70 0.72 0.74 0.76 0.78 0.80 0.82 0.84 0.86 0.88 0.90 0.92 0.94 0.96 0.98 1.00 freq, GHz April 2012  2006 by Fabian Kung Wai Lee 91 Example 5.1 Cont… • The resonator design S-PARAMETERS PARAMETER SWEEP ParamSweep Sweep1 SweepVar="Vcontrol" SimInstanceName[1]="SP1" SimInstanceName[2]= SimInstanceName[3]= SimInstanceName[4]= SimInstanceName[5]= SimInstanceName[6]= Start=0.0 Stop=3 Step=0.5 S_Param SP1 Start=0.7 GHz Stop=1.0 GHz Step=1.0 MHz April 2012 L L2 L=33.0 nH R= 100pF_NPO_0603 C2 VAR VAR1 Vcontrol=0.2 L L1 L=10.0 nH R= Vvar V_DC SRC1 Vdc=Vcontrol V Var Eqn BB833_SOD323 D1  2006 by Fabian Kung Wai Lee C C3 C=0.68 pF Term Term1 Num=1 Z=50 Ohm 92 46 Example 5.1 Cont… • The resonator reactance -X1 of the destabilized amplifier 120 m1 freq=882.0MHz m1=64.725 Vcontrol=0.000000 -imag(VCO_ac Z(1,1)) imag(Z(1,1)) 100 80 m1 60 40 Resonator reactance as a function of control voltage The theoretical tuning range 20 0.70 0.75 0.80 0.85 0.90 0.95 1.00 freq, GHz April 2012  2006 by Fabian Kung Wai Lee 93 Example 5.1 Cont… • The complete schematic with the harmonic suppression filter TRANSIENT Tran Tran1 StopT ime=1000.0 nsec MaxTimeStep=1.0 nsec DC Low-pass filter t VtPWL Src_trigger V_T ran=pwl(time, 0ns,0V, 1ns,0.1V, 2ns,0V) DC DC1 V_DC SRC1 Vdc=3.3 V R RB R=33 kOhm b82496c3120j000 L3 param=SIMID 0603-C (12 nH +-5%) 100pF_NPO_0603 Cc2 b82496c3150j000 L4 param=SIMID 0603-C (15 nH +-5%) b82496c3100j000 L1 param=SIMID 0603-C (10 nH +-5%) 4_7pF_NPO_0603 C Cc1 C6 C=2.2 pF b82496c3330j000 L2 param=SIMID 0603-C (33 nH +-5%) Vvar R R1 R=100 Ohm V_DC SRC2 Vdc=1.2 V BB833_SOD323 D1 pb_phl_BFR92A_19921214 Q1 2_7pF_NPO_0603 C8 C C5 C=0.68 pF C C7 C=3.3 pF 0_47pF_NPO_0603 C9 R RL R=100 Ohm R RE R=100 Ohm 100pF_NPO_0603 C4 April 2012  2006 by Fabian Kung Wai Lee 94 47 Example 5.1 Cont… • The prototype and the result captured from a spectrum analyzer (9 kHz to GHz) Fundamental -1.5 dBm April 2012 Harmonic VCO suppression filter - 30 dBm  2006 by Fabian Kung Wai Lee 95 Example 5.1 Cont… • Examining the phase noise of the oscillator (of course the accuracy is limited by the stability of the spectrum analyzer used) -0.42 dBm Span = 500 kHz RBW = 300 Hz VBW = 300 Hz 300Hz April 2012  2006 by Fabian Kung Wai Lee 96 48 Example 5.1 Cont… • VCO gain (ko) measurement setup: Variable power supply V_DC SRC1 Vdc=3.3 V R RB R=33 kOhm b82496c3150j000 L4 param=SIMID 0603-C (15 nH +-5%) 100pF_NPO_0603 Cc2 b82496c3100j000 L1 param=SIMID 0603-C (10 nH +-5%) R Rattn R=50 Ohm 4_7pF_NPO_0603 Cc1 C C5 C=0.68 pF Vvar Port Vcontrol Num=1 b82496c3120j000 L3 param=SIMID 0603-C (12 nH +-5%) R Rcontrol R=1000 Ohm C C6 C=2.2 pF C C7 C=3.3 pF BB833_SOD323 D1 April 2012 pb_phl_BFR92A_19921214 Q1 2_7pF_NPO_0603 C8 Port Vout Num=2 Spectrum Analyzer 0_47pF_NPO_0603 C9 R RE R=100 Ohm  2006 by Fabian Kung Wai Lee 97 Example 5.1 Cont… • Measured results: fVCO / MHz 950 900 850 ko ≅ 55 MHz = 40.74 MHz/Volt 800 1.35 Volt 750 0.0 April 2012 0.5 1.0 1.5 2.0 2.5  2006 by Fabian Kung Wai Lee 3.0 3.5 4.0 Vcontrol/Volts 98 49 ... while studying for our basic electronics classes Oscillators can be classified into two types: (A) Relaxation and (B) Harmonic oscillators Relaxation oscillators (also called astable multivibrator),... waves Harmonic oscillators are capable of producing near sinusoidal output, and is based on positive feedback approach Here we will focus on Harmonic Oscillators for RF systems Harmonic oscillators. .. steady-state condition is reached when A(s)F(s) = Note that this is a very simplistic view of oscillators In reality oscillators are non-linear systems The steady-state oscillatory condition corresponds
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