Case Study: Osc2 Design of a C-Band VCO

MICROWAVE AND RF DESIGN Case Study: Osc2 Design of a C-Band VCO Presented by Michael Steer Reading: Chapter 20, 20.5,6 Index: CS_Osc2 Based on material in Microwave and RF Design: A Systems Approach, 2 nd Edition, by Michael Steer. SciTech Publishing, 2013. Presentation copyright Michael Steer

Case Study Osc2: Design of a C-Band VCO 4.4 to 5.5 GHz Oscillator Vtune 3.6nH 8.2nH 8.2nH 0.5pF 0.5pF D1 D2 D3 10pF 47.5 Ca 2.2nH Vout 2.2pF Z L 8.2nH L CHOKE Cb Vcc I cc 10pF 10pF 8.2nH D4 TL 1 2k 10pF Slides copyright 2013 M. Steer. 2

Outline Reflection oscillator principles Common base Colpitts oscillator Reflection oscillator operation Resonator and active network topologies Point of oscillation 3

Reflection oscillator Γ r Γ d Y r = G r +jb r Tank V Y d = G d +jb d Device At the frequency and amplitude of oscillation: Y r Y d 1 1 r d When the oscillation signal is small, i.e. for oscillation start-up: r d All equivalent. d d r gets smaller as the oscillation signal builds up. 4

Common base Colpitts oscillator The C R and L R circuit is called a resonator but resonate at a frequency below the oscillation frequency so the network looks like an effective capacitance. C 1 L 3 Vtune C 2 Lchoke C R L R L 3 L B C B C 1 Output R L Drain source Capacitance (could also add additional capacitance) Feedback output C 2 V in H L V out Colpitts Transistor Configuration Colpitts Oscillator Feedback Form 5

Reflection oscillator operation Vtune Lchoke C R L R L B C B Output R L Conductance G r Ideal G d As the amplitude of the oscillation increases, the magnitude of the device conductance, G d decreases while the conductance of the tank circuit, G r is constant. Amplitude A Y r = G r +jb r Tank One port oscillator Y d = G d +jb d Device Susceptance Ideal B r B d As the frequency of the oscillation increases the susceptance of the tank circuit, B r, changes while, B d (ideally) does not change. Frequency, f 6

Active device ideal response Y r = G r +jb r Tank One port oscillator Y d = G d +jb d Device G d B d Results in constant amplitude across the tuning range. Results in low phase noise. Frequency, f Results in low phase noise. B d Amplitude G d A A small variation in B d with respect to frequency is ok (and unavoidable at RF). Also often necessary for oscillator start up., especially for VCOs 7

Common base Γ r Γ d oscillator Y r = G r +jb r V Y d = G d +jb d Tank Device Lchoke Vtune Output C R L R L B C B R L Resonator network Active network Vtune 3.6nH 8.2nH 8.2nH 0.5pF 0.5pF D1 D2 D3 10pF 47.5 Ca 2.2nH Vout 2.2pF Z L 8.2nH L CHOKE Cb Vcc I cc 10pF 10pF 8.2nH D4 TL 1 2k 10pF 8

Resonator network Vtune Lchoke C R L R Inductors are RF open circuits. L B C B Output R L V tune 10pF Resonator network 3.6nH 0.5pF 0.5pF D 1 8.2nH D 2 8.2nH D 3 8.2nH D 4 TL 1 Active network 10pF 47.5 C a 2k 2.2nH V out 2.2pF 10pF Cb Z L 50 8.2nH L CHOKE 47.5 V cc I cc 10pF D1 Vtune D2 D3 D4 r Stacked varactor diodes increase RF breakdown voltage. (Varactors have tunable capacitance.) Transmission line replaces L R and has lower loss. 9

Resonator reflection coefficient V tune D 1 D 2 r 3 GHz 6 GHz 4 GHz V tune 3 V D 3 D 4 r 5.0 GHz Increasing frequency 10

Active network Ideal G d V tune Resonator network 3.6nH 0.5pF 0.5pF D 1 8.2nH D 2 8.2nH D 3 Active network 10pF 47.5 C a 2.2nH V out 2.2pF Cb Z L 50 8.2nH L CHOKE 47.5 V cc I cc 10pF B d 10pF 8.2nH D 4 TL 1 2k 10pF Amplitude A RF SHORT V out Z L V cc RF OPEN C a C b RF SHORT d RF SHORT C a and C b adjust d so that B d V 0 11

Active device reflection coefficient 6 GHz V out Z L V cc d Increasing frequency Increasing signal level 3 GHz 1/ d (Small signal) 12

Γ r Γ d Oscillation point 6 GHz Y r = G r +jb r V Y d = G d +jb d 3 GHz 6 GHz 4 GHz Increasing amplitude Tank Device Intersection defines oscillation frequency and amplitude. r r (3 V) Increasing frequency Want just one intersection for single frequency oscillation. Rotation in opposite directions and with parallel trajectories results in low phase noise. 3 GHz 5.0 GHz d Intersection Increasing frequency 13

Y r = G r +jb r Tank Γ r V Γ d Oscillation point Y d = G d +jb d Device Oscillation condition: Y G r r Y d Gd Br Bd 3 GHz 6 GHz r r (3 V) 4 GHz d Large amplitude 6 GHz Increasing frequency Note that f B d 0 f B r So phase noise is even better than ideal situation. 0 Increasing frequency 5.0 GHz 3 GHz Intersection 14

Summary Topology outlined. Initial design objective stated. Goal is stable single frequency oscillation with low phase noise and high efficiency. To consider next: Detailed design strategy. Oscillator start-up requirements. Strategies for avoiding multiple oscillations. 15

Case Study Osc2: Part B Oscillation Conditions Y r = G r +jb r Tank Y d = G d +jb d Device If stable single frequency oscillation occurs, then Gd G and r That is, 1, 1/, or 1/ r d r d 1. Oscillation condition (variation of conductance and susceptance) Known as Kurokawa oscillation condition 2. Conditions for start up of oscillation Slides copyright 2013 M. Steer. d r B d B r ADA 16

Kurokawa oscillator condition Kurokawa condition for stable singlefrequency oscillation: G B B G d r d r V V VV, 0 0 The subscript 0 refers to the operating point. 0 Y r = G r +jb r Tank V Y d = G d +jb d Device G d Describes a single crossing of the reflection coefficient curves For a fixed frequency RF oscillator G r is very small so second term is negligible. Kurokawa condition simplifies to: G V d B r V V, 0 0 0 G r Amplitude B r B A d For an RF VCO, G r is not small due to varactor loss. So design can be complex. Gr Frequency, G d f 17

Kurokawa oscillator condition for G B B G microwave VCO design Kurokawa condition for stable singlefrequency oscillation: d r d r V V VV, 0 0 0 Y r = G r +jb r Tank V Y d = G d +jb d Device Achieving single-frequency oscillation can be a challenge for microwave fixed frequency oscillator design, and the design complexity is much higher for a microwave VCO. Design using the full Kurokawa condition is found to be too limiting at microwave frequencies. There are other considerations such as minimizing phase noise, e.g. we want the frequency of oscillation to be independent of the oscillation amplitude (this minimizes phase noise). minimizing DC power consumption. conditions for oscillator start-up. 18

Kurokawa oscillator condition simplification Kurokawa condition for stable singlefrequency oscillation: G B B G d r d r V V VV, 0 0 0 Y r = G r +jb r Tank V Y d = G d +jb d Device So in VCO design the design procedure must be kept simple, and this opens up the design space to enable optimization of other characteristics. Microwave VCO design strategy: choose a topology that Has an effective device susceptance that is independent of signal amplitude (i.e., B d / V = 0). Has a loaded resonator conductance that is independent of frequency (i.e., G r / ω = 0). Kurokawa condition for simplified design: G V d B r V V, 0 0 0 19

Simplified Kurokawa oscillator condition Kurokawa condition for simplified design: G V d B r V V, 0 0 0 Y r = G r +jb r Tank Γ r V Γ d Y d = G d +jb d Device r d d d Design device network so that V B d G r 0 Design tank network so that 0 d d Recall unmodified Kurokawa condition: G B B G d r d r V V VV, 0 0 0 20

Alternative simplified Kurokawa Kurokawa condition for simplified design: G V d B r V V, oscillator condition 0 0 0 Y r = G r +jb r Tank Γ r V Γ d Y d = G d +jb d Device r d 21

Simplified Kurokawa oscillator condition r r d d d d d d Fixed frequency oscillator Very little loss in resonator Voltage controlled oscillator Significant resonator loss (due to varactor diodes) 22

Common base Colpitts oscillator Γ r Γ d Lchoke Vtune Output C R L R L B C B R L Resonator network Active network Vtune 3.6nH 8.2nH 8.2nH 0.5pF 0.5pF D1 D2 D3 10pF 47.5 Ca 2.2nH Vout 2.2pF Z L 8.2nH L CHOKE Cb Vcc I cc 10pF 10pF 8.2nH D4 TL 1 2k 10pF 23

Colpitts point of oscillation r r d d d d d 1 2 POINT OF OSCILLATION HERE OR HERE For a fixed frequency oscillator either region of oscillation is suitable. For a microwave VCO region 2 is required because of resonator loss. d 24

Resonator network Vtune Lchoke C R L R Inductors are RF open circuits. L B C B Output R L V tune 10pF D1 Resonator network 3.6nH 0.5pF 0.5pF D 1 8.2nH D 2 8.2nH D 3 8.2nH D 4 TL 1 Active network 10pF 47.5 C a 2k 2.2nH V out 2.2pF 10pF Cb Z L 50 8.2nH L CHOKE 47.5 V cc I cc 10pF Vtune D2 D3 D4 r Stacked varactor diodes 25

Simulated reflection coefficient of the resonator, Γ r, of the C-band VCO. Inductors are RF open circuits. 3 GHz 6 GHz 4 GHz 3.3 GHz D 1 r(1 V) V tune D 2 D 3 D 4 r 5.0 GHz Stacked varactor diodes 26

Reflection coefficient of the resonator at different biases Legend r (1 V) 4.5 GHz r (3 V) 4.5 GHz 6 GHz 6 GHz 3 GHz 3 GHz 3.3 GHz 4.2 GHz 4.5 GHz 4.3 GHz 4.6 GHz 3.7 GHz r (1 V) 4.7 GHz 4.4 GHz D 1 r (3 V) V tune D 2 D 3 D 4 r 5.0 GHz 4.8 GHz 4.5 GHz 4.7 GHz 4.9 GHz 4.6 GHz 27

Comparison of oscillation points Oscillator Case Study #1 Oscillator Case Study #2 6 GHz 3 GHz 4 GHz 3.3 GHz r(1 V) 20 GHz r 15 GHz 5.0 GHz Point of oscillation in this region. Point of oscillation in this region. 28

Required angle of device Y r = G r +jb r Tank Y d = G d +jb d Device R P = 1/G r Conductance G r G d Amplitude A Want high R P = 1/G r so G r is small. (a) Γ d = 1.4 (b) Γ d = 2 (c) Γ d = 4 versus the device reflection coefficient angle. (d) is the oscillator Q for Γ d = 2. 29

Summary oscillation conditions 1. Kurokawa condition for stable single-frequency oscillation: G B B G d r d r V V VV, 0 0 r 0 d d d 2. Simplified Kurokawa condition (easy to design to): G V d B r V V, 0 0 Require that ( B d / V = 0) and ( G r / ω = 0). (If lossy resonator.) Voltage controlled oscillator Significant resonator loss (due to varactor diodes) 0 d d 3. Condition for oscillator start up (for a VCO with a lossy resonator). 30

Kurokawa oscillator condition simplification Kurokawa condition for stable singlefrequency oscillation: G B B G d r d r V V VV, G V d B r V V, 0 0 0 0 Kurokawa condition for simplified design: 0 0 V B d Y r = G r +jb r So, ideally want 0 Tank and Γ r Γ d V G r Y d = G d +jb d Device 0 Also want Keeps phase noise low as oscillation frequency does not depend on amplitude. -B d and G r G d G d is +ve so V B r must be +ve B r Amplitude Amplitude 32

Resonator characteristic Γ r Γ d So, B r G r 0 must be +ve Y r = G r +jb r Tank V Y d = G d +jb d Device Line of constant conductance Also r No dependence on amplitude Conductance G r B r Amplitude A Increasing frequency 33

Resonator characteristic Γ r Γ d r Y r = G r +jb r V Y d = G d +jb d Tank Device Oscillator start up. Also tunable, must be able to rotate r by varying a tuning voltage. 34

Resonator design r Vtune Lchoke C R Γ r L R Γ d L B C B Tank Device 1. Keep resonator as a simple parallel LC circuit. Br 2. L R and C R result in high and can control magnitude. 3. G R comes from L R (transmission line) and C R (varactor). 4. Dependence of G r and B r on amplitude comes from varactor. 35

Resonator network design Lchoke Γ r Γ d Vtune C R Tank L R L B Device DC block Wide (low impedance) microstrip transmission line. Inductor is an RF open circuit. V + I Cj Vtune V D r A reversed biased diode is a variable capacitor. varactor diode 36

Varactor diode, V tune Vtune D RF signal. Want negligible current flow (low shot noise). + V V B I I V tune I 0 V 1. Choose V RF signal. tune to minimize DC current. 2. Minimize current flow and G r. 3. But a good resonator will have a large RF voltage swing. 4. Make sure V tune minimizes current flow. What if RF voltage swing is too large? Cj V tune V Recall that we want V B d 0 37

Varactor stack reduces V B r 0 RF signal. RF signal. D 1 Vtune V tune D 2 D 3 D D 4 RF signal. Cj RF signal. C eff V tune V 4V tune V RF 38

Varactor stack reduces G and r V G r Vtune V tune + V I I Greater tuning range since high current regions can be avoided. I V B 4V B I 0 V RF I 0 V RF Cj C eff V tune VRF V tune VRF 4 39

Varactor stack increases tuning range Vtune V tune + V I I Greater tuning range since high current regions can be avoided. I V B 4V B I 0 V RF I 0 V RF Cj C eff V tune VRF V tune VRF 4 40

D 1 Final resonator V tune D 2 D 3 D 4 r Adjustable short circuit 41

Adjustments RF chokes Capacitance adjustment (also DC block) A V tune DC block D 1 D 2 D 3 D 4 C B r Model A B TL Provide impedance transformation. C TL 42

Reflection coefficient of the resonator at different biases D 1 D V 2 tune D 3 D r 4 Legend r (1 V) 4.5 GHz r (3 V) 4.5 GHz 6 GHz 4.2 GHz 6 GHz 4.5 GHz 3 GHz 3 GHz 4.3 GHz 3.3 GHz 4.6 GHz 3.7 GHz r (1 V) 4.4 GHz 4.7 GHz r (3 V) If crossover of r and 1/ d is as shown by then changing the tuning voltage from 1 V to 3 V changes the oscilaltion frequency from 4.5 GHz to 4.8 GHz. 4.7 GHz 5.0 GHz 4.9 GHz 4.6 GHz 4.8 GHz 4.5 GHz 43

Summary: final resonator network D1 A B Vtune Transmission line reduces loss compared to an inductor Varactor stack reduces resonator conductance. Varactor stack reduces dependence of resonator admittance on signal amplitude. D2 D3 D4 C TL 1 r Adjustments provided by A, B and C B fixed after layout 44

Active network operation Output B d G d Keep G d independent of amplitude to reduce phase noise. L B C B R L Amplitude A Y r = G r +jb r Tank One port oscillator Y d = G d +jb d Device (a) (b) B r B d Curve (a) is simple ideal response, curve (b) response is even better. Frequency, f 47

Active network Ideal Output L R C B L B R L V tune 10pF Resonator network 3.6nH 0.5pF 0.5pF D 1 8.2nH D 2 8.2nH D 3 8.2nH D 4 TL 1 Active network 10pF 47.5 C a 2k 2.2nH V out 2.2pF 10pF Cb Z L 50 8.2nH L CHOKE 47.5 V cc I cc 10pF The resistors are required for biasing. RF SHORT V out Z L V cc RF OPEN C a C b RF SHORT d RF SHORT C a and C b adjust d so that B d and d ( f ) V 0 is parallel to r ( f ). 48

G V Kurokawa oscillator condition Kurokawa condition for simplified design: d B r V V, 0 0 0 Y r = G r +jb r Tank Γ r V Γ d Y d = G d +jb d Device r d d Design device circuit so that B d V 0 d and G d 0 d d Oscillation startup 49

Small and large signal 1/ d r d d d d d Want 1. 2. Large G d at small signal levels. ( 1/ d is small at a small signal level). V B d G d 0 3. (uniform 0 (fast start up of oscillation) (low phase noise) amplitude of oscillation across tuning range ) Increasing frequency Increasing amplitude 50

Reflection coefficient Legend AA C a = 0.5 pf, C b = 0 BB C a = 0.5 pf, C b = 0.5 pf CC C a = 0, C b = 0.5 pf DD C a = 0, C b = 0 6 GHz 4 GHz 1/ d A 6 GHz B C shaping 3 GHz D 3.7 GHz Simulated reflection coefficient of the resonator, Γ r, and the inverse of the small signal reflection coefficient of the active device, 1/Γ d, of the C band VCO for various values of the compensation capacitors C a and C b. 3 GHz 1/ d B C r (3 V) 5.0 GHz A D 51

Increasing 1/ d B 6 GHz amplitude 6 GHz 4 GHz 3 GHz 3.7 GHz Simulated reflection coefficient C a = 0.5 pf C b = 0.5 pf. r (3 V) Increasing oscillation level 5.0 GHz B 3 GHz 1/ d 52

Multiple crossings 6 GHz 4 GHz 6 GHz 1/ d V out Z L V cc 3 GHz C a C b 3.7 GHz d Increasing Simulated reflection coefficient of the resonator, Γ r, and the inverse of the small signal reflection coefficient of the active circuit, 1/Γ d, with C a = 0.5 pf and without C b. 3 GHz r (3 V) 5.0 GHz 1/ d level 53

Multiple simultaneous oscillation 6 GHz 4 GHz 6 GHz 1/ d 3 GHz Measured 3.7 GHz r (3 V) Increasing level 5.0 GHz 3 GHz 1/ d C a = 0.5 pf C b = 0 pf 54

Active network V out Z L V cc d Pi attenuator (with 294 Ω resistors in the shunt legs and a 17.4 Ω series resistor). The output filter is a 50 Ω BPF. 55

Summary: active network design C a V out Z L V cc C b Active network needs to be optimized using measurements (cannot model sufficiently). C a and C b enable shaping d of 1/ d Circuit at RF: C a V out Z L RF OPENV cc C b Need to avoid multi oscillation. Need G d independent of frequency. (Constant amplitude oscillation.) Need large G d for fast startup. d 56

VCO schematic V tune Resonator network 3.6nH 0.5pF 0.5pF D 1 8.2nH D 2 8.2nH D 3 Active network 10pF 47.5 C a 2.2nH V out 2.2pF Cb Z L 50 8.2nH L CHOKE 47.5 V cc I cc 10pF 10pF 8.2nH D 4 TL 1 2k 10pF (a) Adjustable features V out Z L V cc d L (b) D 1 V tune D 2 D 3 D 4 r (c) 58

Final VCO circuit Resonator network Active network Adjustable features 59

Resonator and active device circuits. Resonator network Active network 60

Measurement of the active network Measurement of the active circuit with a 50 Ω test fixture at the interface of the resonator and active networks. The card was cut at the interface to make the connection. The 35 ps delay is due to the length of the SMA connector is required to reference measurements to the circuit card edge. The period of a 5 GHz signal is 200 ps. So the connector has an electrical length of 63 o. The reflection coefficient is rotated by 126 o. So measurements must be corrected. The SMA connector also has parasitic capacitance and inductance. Correction will not be perfect. 61

Resonator measurements 3 GHz 6 GHz 5.3 GHz Corrected Measured Γ r at 3 V. r 3.8 GHz Raw Actual measurements rotated by 126 o 62

6 GHz Measurement Measured Γ r at 3 V. C a = 0.5 pf and C b = 0. 1/Γ d moves to the right as the signal level increases. 3 GHz r 4.8 GHz 5.4 GHz 4.4 GHz 5.3 GHz The intersection of 1/Γ d and Γ r determines the oscillation frequency and the signal level. 3.8 GHz 1/ d Small signal 3 GHz

3 GHz 6 GHz 4 GHz 6 GHz Comparison 4.8 GHz 6 GHz 5.3 GHz 3.7 GHz 3 GHz 5.4 GHz 4.4 GHz r Increasing level r 3.8 GHz 5.0 GHz 3 GHz d Simulated 0.4 S 2.5 Measured C a = 0.5 pf and C b = 0. V tune = 3 V Small signal d 3 GHz 64

Simulation and measurement accuracy Simulation fidelity Measurement fidelity 21/2 D EM simulation used but side wall capacitances not taken into account. Model limitations. Connection resistances are not accounted for. Full effect of SMA connector not accounted for. Parasitics of connector Field lines terminate on flange. 65

3 GHz Large signal characteristic 6 GHz d Large signal 10 dbm 6 GHz RR Locus of oscillation 5.3 GHz 3 GHz RR 5.3 GHz r 4.5 GHz a b c d 4.5 GHz 4.8 GHz Γ r for 0V (curve a) to 9 V (curve g) e f g Large signal 1/Γ d. 3.5 GHz 66

Resonator adjustments A A D1 D2 D3 D4 C TL 1 r C Adjustments provided by A, and C 67

Active network adjustments C a and C b enable shaping Circuit at RF: V out Z L V cc of 1/ d C a C b d C a C b 68

Measured tuning curve 69

Measured output power and harmonics At V out (before the bandpass filter) indicating low level harmonic content. 70

Phase noise measured 71

Summary: C band (5 GHz) VCO V tune 10pF 3.6nH 8.2nH 8.2nH 8.2nH 0.5pF 0.5pF D 1 D 2 D 3 D 4 TL 1 10pF 47.5 C a 2.2nH 2k V out 2.2pF 10pF Cb Z L 50 8.2nH L CHOKE 47.5 V cc I cc 10pF Microwave VCO design is a methodical process. Simulation together with measurements leads to a methodical design process. Build in adjustability in design. Microwave circuits nearly always require tuning of each item. 72