Colpitts Oscillator Tutorial

Transcription

1 1 of 10 olpitts Oscillator Tutorial J P Silr john@rfic.co.uk 1 ABSTAT This paper will describe the design and test of a low noise VHF olpitts voltage controlled oscillator (VO), designed to operate at 00MHz (Tuning bandwidth of - 3MHz/V or 1 to 10V ) with an associated phase noise performance of 10KHz. Theory will be gin for the design of the reflection amplifier and high Q resonator, together with the relevant AD simulations to rify the design. DESIGN DESIPTION -1 ESONATO DESIGN [1,] The first part of the design process is to determine the required unloaded Q of the resonator to achie the phase performance of <-100dB/Hz at 10KHz. The simulation shown in Figure 1 simulates the phase noise of an oscillator for a gin loaded Q, Noise figure and frequency. The resulting simulation plot for a VO at 00MHz with a loaded Q of 30 is shown in Figure. PhaseNoiseMo MOD Fnom=fcentre out=50 Ohm Fcorner=10 MHz NF= db QL=30 This simulates the open-loop phase noise the VO Now that we ha a design criteria for the resonator loaded Q (in this case > 30) we could decide on the topography of the resonator E PhaseNoise Phase noise prediction (Bipolar device) assumimg loaded Q of PhaseNoise=10*log(0.5*VO_phasenoise..PNoise_OL.noise* *) m indep(m)=1.000e 4plot_vs(PhaseNoise, noisefreq)= m 1E3 1E4 1E5 noisefreq, Hz 1E6 Phase Noise Mod P_1Tone POT1 Num=1 Z=50 Ohm P=dbmtow(10) Freq=fcentre VO_OL Meas Meas meas1 PNoise_OLout=real(PNoise_OL[0 VO_OLout=VO_OL[ HAMONI BALANE HarmonicBalance HB1 Freq[1]=fcentre Order[1]=7 NLNoiseMode=yes NLNoiseStart=100 Hz NLNoiseStop=1 MHz NoiseNode[1]="PNoise_OL" VA VA3 fcentre=00mh PNoise_OL PM_DemodTune DEMOD Sensitivity=180/p Fnom=fcentre out=50 Ohm Figure esulting simulation of the ADS schematic shown in Figure 1, showing a predicted phase noise of 94dBc/Hz at 10KHz for a loaded Q of > 30. The unloaded/loaded Q of the resonator depends on the values of the L/ ratio of the tank circuit and on the unloaded Q s of the individual components. Typically, ceramic microwa capacitors such as the AT100a range (by American technical ceramics) ha unloaded Q s of between 00 and 1000 with capacitor values up to 10pF. Unfortunately inductor Q s are considerably less, for example the oilcraft 0805S series ha unloaded Q s of between and thus are the limiting factor on resonator loaded Q. Figure 1 ADS simulation to determine the minimum loaded Q of the resonator required to meet a specific phase noise requirement.

2 of 10 -TWO ELEMENT ESONATO IUIT [] Figure 3 shows a schematic diagram of a two-element resonator. This circuit is seldom used in oscillators as the loaded Q will be ry low as the source and load impedances will directly load the tuned circuit. Q =. ω.l c Frequency Tuning network Q = ω. L. Figure 3 Schematic of a two element, lumped resonator, together with loaded Q equations. The assumes that the circuit is terminated in both a source and load impedance (value ) At resonance the transmission phase is zero and the network is loss less (except for the resistance of the inductor). The series resonator impedes signal transmission while the parallel network allows signal transmission. The main problem with such a simple resonator is achieving a required Q, for example if we want a Q of 30 we would need the following series inductor & capacitor at 00MHz:..Q L = ω 1 πf = L = * 50 * 30 π * 00E 1 π * 00E = 6.3E 6 6 =.3uH = 0.7pF The problem with this circuit is that the loaded/unloaded Q and phase of the network are interdependent and therefore it is better to lightly couple the resonator by using a capacitor so that the unloaded Q of the resonator is effectily separated from the load impedance load, which would normally greatly reduce the Q of the resonator. The addition of the coupling capacitor c to the resonator, will allow us to change the loaded Q of the circuit without greatly effecting the resonant frequency. This arrangement is shown in Figure 7. In addition if frequency control is required then the varactor network shown can be added in parallel with the tuned circuit. Figure 4 Modified L- resonator with oupling capacitor c added to isolated the unloaded Q of the resonator with the applied load. In addition the varactor network can be added to gi frequency tuning. The bandwidth of the frequency controlled network is adjusted by the capacitor in series with the varactor. The easiest way to determine the maximum oupling capacitor c is by way of the simulation shown in Figure 5. Note that an arbitrary inductor value has been chosen and the apacitor is used to resonate it at 00MHz. It is better to ha a higher value of resonating capacitor so that the effect of the oupling apacitance (c) on the resonator frequency is minimized. Port P1 Num=1 S_Param SP1 enter=00 MHz Span=00 MHz VA VA1 c=1.0 Term Ter APQ Num=1 3 Z=50 Ohm =c pf F=00.0 MHz S-PAAMETES ParamSweep Sweep1 Sweep="c" Start=1.5 Stop=6 PAAMETE SWEEP APQ INDQ =3.3 pf L1 L=100 nh F=00 MHz Q=60 F=00 MHz dc=0.0 Ohm Figure 5 ADS simulation to vary the value of c to determine the resonator loaded Q. Note the S-parameter block needs the Group Delay parameter checked. The resulting simulation plot is shown in Figure 6. The plots show us that if we require a loaded Q of > 30 then c must be less than.5pf. But we ha to remember that c will also effect the phase looking into the resonator which we ha to equal to the reflection amplifier phase but with opposite sign. In addition the varactor network will effect the loaded Q and resonator frequency depending on the coupling to the varactor. This coupling determines the capacitance swing and hence tuning bandwidth of the resonator. So a narrow tuning network gis the better Q than a wideband network.

3 3 of 10 j s Ls p Figure 7: Typical equivalent circuit of a varactor diode. The series inductor Ls and parallel capacitor p are package parasitics, typical values are p ~ 0.1pF and Ls = 1.5nH. The general equation for calculating the capacitance of the varactor is: = V 1+ J V V J + γ P Figure 6 esult of simulation shown in Figure 5, showing variation in loaded Q with oupling capacitor c (varied between 1.5pF & 6pF in 0.5pF steps). If we require a loaded Q of > 30 then c must be less than.5pf. Now that we ha determined our basic resonator design we need to determine the values of the varactor network, by choosing a varactor and the correct coupling capacitor to gi us the correct delta for the resonator. From the varactor data sheet we can note the capacitance vs voltage cur and thus generate a varactor model for use in our simulations. -3VAATO MODEL AND TUNING ANGE [3] Voltage variable capacitors or tuning diodes are best described as diode capacitors employing the junction capacitance of a rerse biased PN junction. The capacitance of these devices varies inrsely with the applied rerse bias voltage and is used to vary the centre frequency of the resonator. The equivalent circuit of a typical varactor together with the package parasitics is shown in Figure 7. where : = diode capacitance V V = applied voltage, V = junction contact potential (~ 0.7V) J γ = apacitance exponent V = diode capacitance For the Philips BB405 varactor diode, s is gin as 0.75ohms with capacitances of 18pF@1V, 11pF@3V and pf@8v. For the abo equation the capacitance values equate to a value of γ = 0.74 with J = 35pF (valid for control voltages 1 to 8V). The varactor model was substituted for the fixed capacitor and simulated or a range of tuning voltages to determine the frequency range and tuning constant of the resonator. The easiest way to determine the value of the coupling capacitor is to generate a spreadsheet and enter values of actor coupling capacitor as shown in Table 1. From the table we can see that if we pick a varactor coupling capacitor of 6pF then we should achie our tuning bandwidth of ~ 3MHz/V. Note the addition of the resonator coupling capacitor c will alter these values slightly and some adjustments may need to be made.

4 4 of 10 actor Max ap 14 pf 1.4E-11 actor Min ap 4 pf 4E-1 Enter Tuning range 10 V esonator ap.7 pf.7e-1 esonator Ind 100 nh actor Network actor coupling ap Max Min Min Freq Max Freq Tuning ange (pf) (MHz) (MHz) (MHz/V) Table 1 esult of spreadsheet calculation of varactor coupling capacitor on frequency and tuning bandwidth. If we pick a varactor coupling capacitor of 6pF then we should achie our tuning bandwidth of ~ 3MHz/V. Note the addition of the resonator coupling capacitor c will alter these values slightly and some adjustments may need to be made. We can now put all the components together and simulate the frequency response, Q and tuning range of the resonator before designing the reflection amplifier. For the next simulation shown in the varactor sub-model has been added, which is shown in Figure 8 and a symbol was generated for use in the resonator model shown in Figure 9. Port P1 Num=1 =j pf 3 =0.1 pf VA VA volts=v1 j=35/((1+(volts/0.7))^0.74) 1 =0.75 L L1 L=1.5 nh = Port P Num= Figure 8: ADS sub-model of the BB405 varactor diode. The voltage V1 is passed through to this model at a higher lel. Port P1 Num=1 Figure 9 Using the view create/edit schematic symbol command in ADS, this diode symbol was drawn for use in the resonator network model. S-PAAMETES S_Param SP1 enter=00 MHz Span=100 MHz VA VA1 c=3 Vcntrl=1 Vc=6 APQ 3 =c pf F=00.0 MHz Term Ter Num=1 Z=50 Ohm INDQ L1 L=65 nh Q=60 F=00 MHz dc=0.0 Ohm PAAMETE SWEEP ParamSweep Sweep1 Sweep="Vcntrl" Start=1 Stop=10 APQ =3.3 pf F=00 MHz APQ 4 =Vc pf F=00.0 MHz BB405 X1 V1=Vcntrl Figure 10 ADS schematic of the completed resonator. The sweep parameter box is set to sweep the varactor control voltage between 1 10V and is fed through to the varactor model by V1=Vcntrl. (Note to set the through variable right click on the varactor symbol and select edit component parameters then add the variable V1=Vcntrl). In order to get the correct resonant frequency with the varactor network and coupling capacitor c added the inductor was reduced in value from 100nH to 65nH. The simulated sweep of Q/frequency vs control voltage (Vcntrl) is shown in Figure 11. We can see from the top plot of input return loss (S11) that we need to design a reflection amplifier with at least 8dB of reflection gain to orcome the losses of the resonator. Usually the reflection amplifier is design with greater gain > 3dB extra to gi some margin. The next section will now deal with the design of the reflection amplifier part of the colpitts oscillator design.

5 5 of 10 Iin Vin Zin 1 L Figure 1: Simplified schematic diagram showing the reflection amplifier part of the olpitts oscillator. The capacitor network of 1 and would provide positi feedback from the emitter to base. The steady state loop equations were expanded out, (as shown in the olpitts derivation tutorial) to yield an expression for the negati impedance of this type of amplifier, in terms of the capacitors used for feedback and the transconductance of the acti device: Vin Iin = Zin 1 = - gm. ω 1 + jω[ ( ) Figure 11 The completed resonator plot of Q vs sweep control voltage (Vcntrl). We can see from the top plot that we need to design a reflection amplifier with at least 8dB of reflection gain to orcome the losses of the resonator. 4.8 EFLETION AMPLIFIE DESIGN [4,5,6] The reflection amplifier of the olpitts oscillator was achied by the use of capaciti feedback network as shown in Figure 1. A suitable F medium power bipolar transistor, with a ft of > 1GHz was required and at this low frequency there were seral to choose from including the BF9, BF93, BFY90 and AT For this design the BF9 was chosen. Input impedance (negati) Parallel combination of 1 & And fo = π L 1 [. ( + )] 1 1 As we assumed that X 1 << hie, then 1 should be as large as possible and in order for these feedback components to dominate or the parasitic capacitance s of the transistor should be as large as possible too. gm For sustained oscillatio n s = ω. m Assuming 1 = then m is the product of the two capacitanc e' s. Although we required large values of capacitance to dominate the circuit performance, they were restricted in their size by the following expression:

6 6 of 10 s s gm ω.m G ω.m G ω.m s 1 G ω.m Where G is the maximum value of gm - (the transistors mutual conductance) & s is the input impedance of re - arranging: - s G the resonator 1 ω.m By simulation of the Spice model BF9 at various collector currents, the input resistance (hie) and A current gain (hfe) were determined, in order to calculate the values of gm and G as gin in the previous equations. Figure 13 below shows the HP ADS circuit used to analyse the required parameters and Table shows the resulting values of hie and hfe, for a current of 5mA (load = 1150 ohms): 5 =1.3 kohm D D1 D S-PAAMETES S_Param SP1 Start=00 MHz Stop=00 MHz 5.19 ma 0 V A Term 0 A Ter D_Block Num=1 D_Block1 Z=50 Ohm Zin N 6.75 V 6.75 V vref 6.75 V VA VA1 load=1000 Zin Zin1 Zin1=zin(S11,PortZ1) 64.3 ua D_Feed D_Feed1 4 =1 kohm 1 V 6.75 V 6.75 V vb 64.3 ua 64.3 ua Ib ircuit to determine hfe,hie & Zin 5.5 ma 0 A 1 =10000 pf ma V_D S1 Vdc=1.0 V pb_sms_bf9p_ Q ma ma 5.95 V 5.95 ma 1 =load 1 V 5.89 ma Ic 1 V 5.89 ma D_Feed D_Feed 0 A D_Block D_Block 0 A Term Term3 Num= Z=50 Ohm Figure 13: HP ADS circuit used to analyse the necessary parameters required calculating the feedback capacitors 1 &. To calculate hfe & hie the values of Ic, Ib, vin & were analysed - hfe = Ic/Ib and hie = (vin-)/ib. By F decoupling the emitter of the transistor, (by use of 1) the input impedance at 00MHz was predicted, by running an S-parameter simulation on the circuit. Ic.i 5.000mA hfe hie ma/v gm in (ohms) Zin / By running the simulation with different values of load a range of parameters are calculated so that the colpitts capacitors can be calculated for a particular current. The table of various load settings is shown in Table 3. Ic (ma) load (ohms) in (ohms) hfe Zin (ohms) Gm (ma/v) Table 3 Simulation summary of the basic amplifier circuit of Figure 13 for various values of load. Values of Input resistance (hie) and (A Gain) hfe for the BF9 transistor for various collector current bias values. Using this data the value of gm was calculated. Using the values shown in Table 3, we could estimate the maximum series capacitance of the combination of 1 and i.e. m at a picked current of 5mA Note the input impedance of the resonator s can be found be re-simulating the resonator with a Zin block and for our example s = 17 ohms 1 r 17 at Ic = 5mA = 51-3 ω.m gm 6.4E 1 At 00MHz m 15pF. 6 π.00e.51 Using initial values of 1 and = 30pF, the reflection amplifier was analyzed using HDADS and the circuit shown in Figure 14. The two feedback capacitors were optimised to produce a reflection gain > 1dB and resulted in capacitor values of 33pF for 1 and. This circuit included the spice model of the BF9, which required biasing to a voltage supply via the F bias components for the simulation to work. A S-parameter analyser box, was added to the schematic to allow the reflection magnitude and phase to be plotted while, the addition of the D analyser box allowed D bias conditions to be predicted at each node. hfe=ic.i/ib.i hie=(vb-)/ib.i gm=(hfe/hie)*1e3 Table Simulation output & equations for the ADS simulation shown in Figure 13

7 7 of 10 00MHz Basic olpitts reflection amplifier 5 4 =1.3 kohm =1 kohm 14 db(s(1,1)) vref 1 D D1 D D_Feed D_Feed1 Isupply V_D S1 Vdc=1.0 V Ic D_Feed D_Feed freq=00.mhz db(s(1,1))= freq, MHz Term Ter Num=1 Z=50 Ohm D_Block D_Block1 1 =39 pf =33 pf Ib vb pb_sms_bf9p_ Q1 1 =1180 Ohm S_Param SP1 Start= Stop= Step= S-PAAMETES enter=00 MHz Span=150 MHz Figure 14: ircuit used to analyse the reflection amplifier, with the additions of the ideal bias components. An S- parameter simulation is run to determine the frequency response of the reflection amplifier s return gain, together with the corresponding value of reflection phase. D_Block D_Block Figure 18 Shows the frequency response of the reflection amplifier part of the olpitts with the feedback capacitors both set to ~ 33pF. The aim was to maximise the reflection gain at the centre frequency of 00MHz, by varying the values of 1 and. This return gain must end up being greater than the return loss of the resonator and in addition, the phase of the resonator must be opposite to the input phase of the reflection amplifier, to ensure oscillation will occur. The circuit was optimised to maximise the gain of the reflection amplifier. This occurred with values of capacitors 1 = 33pF and = 33pF, resulting in a reflection gain of 13.8dB, with a corresponding reflection phase of 67 degrees. 8 =50 Ohm vout phase(s(1,1)) freq, MHz Figure 15 AD analysis of the reflection amplifier with the input bias inductor tuned for best reflection gain. The plot on the left shows return gain in db and the plot on the right shows the return phase in degrees both at 00MHz. With these values of gain there was a ~ 6dB gain margin when the resonator was coupled to the amplifier. The final phase and input return loss plots of the resonator set to the middle of the band ie 00MHz (with a control voltage of 4.3V) is shown in Figure db(s(1,1)) freq=00.1mhz db(s(1,1))= phase(s(1,1)) freq, MHz m m freq=00.1mhz phase(s(1,1))= freq, MHz Figure 16 Shows the phase of the resonator with the control voltage of the varactor set to gi a frequency of 00MHz. The resulting phase is +155 degrees with a return loss of 9.4dB

8 8 of 10 SP1.SP.S(1,1) 4.9 OSILLATO SIMULATION When the two circuit elements (resonator & reflection amplifier) are connected together that the loop phase will be zero. Analysis of the resonator and the reflection amplifier, yielded reflection phases of +155 and 67 degrees respectily. Hower, the reflection phase of the resonator already includes, the coupling capacitor required to gi the correct loaded Q. For oscillation to occur, there must be >1 magnitude at the zero phase point. Ideally this should occur at maximum reflection gain for best performance. The easiest way to evaluate this capacitance & frequency of oscillation is to perform a S-parameter measurement with the resonator and reflection amplifier connect together as shown in Figure 17. VA VA1 c=.0 Vcntrl=4.5 Vc=6 APQ 5 =c pf F=00 MHz APQ 3 =4.7 pf F=00 MHz INDQ L1 L=65 nh Q=60 F=00 MHz dc=0.0 Ohm 00MHz olpitts S-Parameter Oscillation Test 5 =1.3 kohm S- PAAMETES S_Param SP1 enter=00 MHz Span=150 MHz D D1 D OscTest D_Block OscTest1 D_Block1 Port_Number=1 Z=1.1 Ohm Start=100 MHz Stop=300 MHz Points=101 APQ 4 =Vc pf F=00.0 MHz BB405 X V1=Vcntrl vref D_Feed D_Feed1 1 =39 pf =33 pf 4 =1 kohm Ib vb Isupply V_D S1 Vdc=1.0 V pb_sms_bf9p_ Q1 1 =100 Ohm 8 =50 Ohm Figure 17 S-Parameter simulation of the completed olpitts oscillator. The Osctest block has been placed between the resonator & reflection amplifier in order to determine the magnitude & gain at a particular frequency. That s is to say we require a magnitude greater than 1 at zero phase at the operating frequency for oscillation to occur. vout D_Feed D_Feed Ic D_Block D_Block With the OscTest simulator block connected between the resonator and reflection amplifier we can simulate the combined phase and magnitude at the oscillation frequency. The result of the simulation is shown in Figure 18. freq=00.5mhz SP1.SP.S(1,1)=1.09 / freq (15.0MHz to 75.0MHz) Figure 18 esult of the simulation shown in Figure 17. Showing that at 00MHz we do indeed ha a phase of zero and a magnitude greater than 1. (Note the resonator capacitor 3 was adjusted to gi the correct oscillation frequency with the varactor set for mid tuning range. With the circuit rified for oscillation at 00MHz, we could now simulate the two circuits together using nonlinear analysis to obtain phase noise, output power, harmonics and D bias values. The simulation shown in Figure 19 uses a Harmonic Balance simulator to simulate phase noise, output power and frequency performance. A number of parameters need to be set in the harmonic balance simulator box ie: Freq: 00MHz, order 3. Noise(1): Select Log, Start 100Hz, Stop 10MHz, Points/decade 10, Select Include FM noise. Noise() Select vout, Select Non linear Noise & Oscillator Osc Osc Port name Osc1 All other parameters can be left to their default values. The simulation model contained the reflection amplifier based around a spice model of the BF9 together with associated D bias. Note: To make the simulation more accurate and representati of a final design, transmission lines should be added for the component pads and circuit inter-connections.

9 9 of 10 APQ 5 =c pf F=00 MHz Mode=proportional to f APQ 3 =4.4 pf F=00 MHz Mode=proportional to freq INDQ L1 L=65 nh Q=60 F=00 MHz Mode=proportional to dc=0.0 f Oh 5 =1.3 koh HAMONI BALANE HarmonicBalanc ehb1 Freq[1]=00 Order[1]=3 MH NLNoiseStart=100 NLNoiseStop=10.0 H NLNoiseStep MH NoiseOutputPort= FM_Noise=yes OscPortName="Osc1 " OscPort Osc1 V= Z=1.1 Ohm NumOctas= Steps=10 FundIndex=1 MaxLoopGainStep 00MHz olpitts Harmonic Balance D_Block D_Block1 APQ 4 =Vc pf F=00.0 Mode=proportional MH to freq BB405 X V1=Vcntrl vref D_Feed D_Feed1 1 =33 pf =33 pf 4 =1 koh VA VA1 c=.0 Vcntrl=4.5 Vc=6 D D1 Ib D vb Isupply Ic V_D S1 Vdc=1.0 D_Feed V D_Feed pb_sms_bf9p_ Q1 1 =780 Oh D_Block D_Block 8 =50 Ohm Figure 19: Harmonic balance ADS schematic of the olpitts oscillator. The olpitts feedback capacitors and resonator tuning capacitor ha been optimized for frequency and oscillator output power. The simulator uses the Oscport, to inject F into the system to allow prediction of oscillated frequency, power and phase noise. pnfm, dbc vout i.e. < 1KHz will be at least 10dB worse than the simulation due to the device flicker noise which is not defined in the BF9 spice model. Any phase noise below about 150dB/Hz was unlikely to be measured as this lel fell below the measuring system noise floor dbm(hb.vout) m m harmindex=1 dbm(hb.vout)= D.Ic.i 7.58mA harmindex D.vb V D V Figure 1: Harmonic lel output simulation showing harmonic output power (dbm) against the harmonic index. The marker is set to the oscillator fundamental frequency (index=1). The relatily high second harmonic lel required that the following buffer amplifier was fitted with some form of harmonic filter either as part of the output matching circuit or a stand alone low-pass filter. harmindex HB.freq Hz 00.MHz 400.4MHz 600.6MHz noisefreq=10.00khz pnfm=-10. dbc Table 4: Harmonic index against output frequency. This table shows the frequencies of the various harmonic indices gin in the simulation at the top of the page E 1E3 1E4 1E5 1E6 noisefreq, Hz 1E7 Figure 0: Predicted phase noise plot showing phase noise in dbc/hz against carrier offset frequency in Hz. The red line is the simulation result with the blue line showing the required specification. The oscillator was designed to meet the phase noise specification with a 0 db margin. In practice the close to carrier phase noise 8 SUMMAY AND ONLUSION The VO met the requirements of the equipment specification except for the VO tuning bandwidth, which was slightly low at by ~.MHz - Ideally to gi a bit of margin needs to be ~.5MHz/V. This could be increased by increasing the varactor coupling capacitor to the next preferred value.

10 10 of 10 To complete the design a VO buffer amplifier complete with harmonic filter needs to be designed to reduce the output power variations or temperature and remo any loadpulling effects (i.e. a change in oscillating frequency with variations in the output load/match). To eliminate load-pull between the VO and buffer amplifier, an attenuator can be fitted before the buffer amplifier (still ensuring that the buffer amplifier is operated in compression). With the buffer amplifier in compression, (or in limiting) the variations in the VO output power with temperature and control voltage should be greatly reduced. 10 EFEENES [1] adio Frequency Design Wes Hayward, 1994, The American adio elay League, ISBN , p6. [] Oscillator Design and Simulation, andall W hea, 1995, Noble Publishing, ISBN , p [3] Microwa and Wireless Synthesisers Theory and Design, Ulrich L ohde, 1997, Wiley Inter-science, ISBN , hapter. [4] Microwa Engineering David M Pozar, 1993, Addison-Wesley, ISBN , [5] Oscillator Design and Simulation, andall W hea, 1995, Noble Publishing, ISBN , p34.

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