Case Study: Osc2 Design of a C-Band VCO Presented by Michael Steer Reading: Chapter 20, §20.5,6 Based on material in Microwave and RF Design: A Systems Approach, 2 nd Edition, by Michael Steer. SciTech Publishing, 2013. Presentation copyright Michael Steer MICROWAVE AND RF DESIGN Index: CS_Osc2 Case Study Osc2: Design of a C-Band VCO Slides copyright 2013 M. Steer. 2 4.4 to 5.5 GHz Oscillator 2k 47.5 TL 1 10pF 2.2nH 10pF 2.2pF 3.6nH 8.2nH 8.2nH 8.2nH 0.5pF 0.5pF 10pF 10pF 8.2nH CHOKE L C a C b V out Z L V tune D 1 D 3 D 4 D 2 V cc I cc Outline ● Reflection oscillator principles ● Common base Colpitts oscillator ● Reflection oscillator operation ● Resonator and active network topologies ● Point of oscillation 3 Reflection oscillator r Y = G +jB r r d Y = G +jB d d Device Tank V Γ r Γ d At the frequency and amplitude of oscillation: r d Y Y 1 r d 1 r d When the oscillation signal is small, i.e. for oscillation start-up: d r gets smaller as the oscillation signal builds up. d All equivalent. 4
Transcript
Case Study:Osc2Design of aC-Band VCO
Presented by Michael Steer
Reading:Chapter 20, §20.5,6 Based on material in Microwave and RF
Design: A Systems Approach, 2nd Edition, by Michael Steer. SciTech Publishing,
2013.Presentation copyright Michael Steer
MICROWAVE AND RF DESIGN
Index: CS_Osc2
Case Study Osc2:Design of a C-Band VCO
Slides copyright 2013 M. Steer.2
4.4 to 5.5 GHz Oscillator
2k
47.5
TL110pF
2.2nH
10pF
2.2pF3.6nH
8.2nH
8.2nH
8.2nH
0.5pF 0.5pF
10pF
10pF
8.2nHCHOKEL
Ca Cb
VoutZL
Vtune
D1
D3
D4
D2
VccIcc
Outline● Reflection oscillator principles● Common base Colpitts oscillator● Reflection oscillator operation● Resonator and active network topologies● Point of oscillation
3
Reflection oscillator
rY = G +jBrr dY = G +jBdd
DeviceTank
V
Γr Γd
At the frequency and amplitude of oscillation:
r dY Y 1r
d
1r d
When the oscillation signal is small, i.e. for oscillation start-up:
d r gets smaller as the oscillation signal builds up.d
All equivalent.
4
Common base Colpitts oscillator
LBRL
CBCR LR
chokeLOutputVtune
The CR and LR circuit is called a resonator but resonate at a frequency below the oscillation frequency so the network looks like an effective capacitance.
C2C1
L 3
C2
C1L 3 Feedback output
Colpitts Oscillator Feedback Form
ColpittsTransistor Configuration
H
Vin outVL
Drain sourceCapacitance (could also add additional capacitance)
5
Reflection oscillator operation
One‐port oscillator
As the amplitude of the oscillation increases, the magnitude of the device conductance, |Gd|decreases while the conductance of the tank circuit, Gr is constant.
As the frequency of the oscillation increases the susceptance of the tank circuit, Br, changes while, Bd (ideally) does not change.
rY = G +jBrr dY = G +jBdd
DeviceTank Bd
Sus
cept
ance
Frequency, f
rB
Gd
Con
duct
ance
G
Amplitude A
r
6
LBRL
CBCR LR
chokeLOutputVtune
Ideal
Ideal
Active device ideal response
One‐port oscillator
rY = G +jBrr dY = G +jBdd
DeviceTank Bd
Frequency, f
dG
Gd
B
Amplitude A
d
7
Results in low phase noise.
A small variation in Bdwith respect to frequency is ok (and unavoidable at RF). Also often necessary for oscillator start‐up., especially for VCOs
Results in constant amplitude across the tuning range.
1. Oscillation condition (variation of conductance and susceptance)Known as Kurokawa oscillation condition
2. Conditions for start‐up of oscillation
d rG G If stable single‐frequency oscillation occurs, then and d rB B
1/r d That is, , , or 1/d r 1r d
Kurokawa oscillator condition
0 0,
0d dr r
V V
G BB GV V
Kurokawa condition for stable single-frequency oscillation:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
The subscript 0 refers to the operating point.
Describes a single crossing of the reflection coefficient curves
For a fixed frequency RF oscillator Gr is very small so second term is negligible.
Kurokawa condition simplifies to:
17
For an RF VCO, Gr is not small due to varactor loss. So design can be complex.
0 0,
0d r
V V
G BV
Gd
G
Amplitude A
r
B
Frequency, f
rB
d
rGGd
Kurokawa oscillator condition for microwave VCO design
0 0,
0d dr r
V V
G BB GV V
Kurokawa condition for stable single-frequency oscillation:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
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
0 0,
0d dr r
V V
G BB GV V
Kurokawa condition for stable single-frequency oscillation:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
So in VCO design the design procedure must be kept simple, and thisopens 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., ∂Bd /∂V = 0).• Has a loaded resonator conductance that is independent of
frequency (i.e., ∂Gr/∂ω = 0).
190 0,
0d r
V V
G BV
Kurokawa condition for simplified design:
Simplified Kurokawa oscillator condition
0 0,
0d r
V V
G BV
Kurokawa condition for simplified design:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
r
d
d
d
dd
Γr Γd
0dBV
Design tank network so that 0rG
0 0,
0d dr r
V V
G BB GV V
Recall unmodified Kurokawa condition:
20
Design device network so that
Alternative simplified Kurokawaoscillator condition
0 0,
0d r
V V
G BV
Kurokawa condition for simplified design:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
r
d
Γr Γd
21
Simplified Kurokawa oscillator condition
r
d
22
r
d
d
d
dd
Fixed frequency oscillatorVery little loss in resonator
Voltage controlled oscillatorSignificant resonator loss (due to varactor diodes)
Active networkResonator network
2k
47.5
TL110pF
2.2nH
10pF
2.2pF3.6nH
8.2nH
8.2nH
8.2nH
0.5pF 0.5pF
10pF
10pF
8.2nHCHOKEL
Ca Cb
VoutZL
Vtune
D1
D3
D4
D2
VccIcc
Common base Colpitts oscillator
LBRL
CBCR LR
chokeLOutputVtune
23
Γr Γd
Colpitts point of oscillationr
d
24
r
d
d
d
dd
POINT OF OSCILLATIONHERE
1 2For a fixed frequency oscillator either region of oscillation is suitable.For a microwave VCO region 2 is required because of resonator loss.
OR HERE
(x)
Active networkResonator network
(x)
(x)
r
Vtune
D1
D3
D4
D2
50
47.5
2k
47.5
TL 1
(x)
10pF
2.2nH
10pF2.2pF
3.6nH
8.2nH
8.2nH
8.2nH
0.5pF 0.5pF
10pF
10pF
8.2nHCHOKEL
Ca Cb
VoutZL
V tune
D1
D3
D4
D2
VccI cc
Resonator network
LBRL
CBCR LR
chokeLOutputVtune
Stacked varactordiodes
Inductors are RF open circuits.
25
Simulated reflection coefficient of the resonator, Γr, of the C-band VCO.
26
(x)
(x)
r
Vtune
D1
D3
D4
D2
Stacked varactor diodes
Inductors are RF open circuits.
5.0 GHz
r
3.3 GHz
6 GHz4 GHz
(1 V)
3 GHz
4.8 GHz
5.0 GHz
4.6 GHz
4.5 GHz
r (1 V)
4.5 GHzr (3 V)r (1 V)
4.9 GHz
4.6 GHz
4.4 GHz
4.3 GHz
4.2 GHz
4.7 GHz
Legend4.5 GHz
4.7 GHz
3.7 GHz
3 GHz
6 GHz3 GHz
3.3 GHz
6 GHz
4.5 GHz
r (3 V)
Reflection coefficient of the resonator at different biases
27
(x)
(x)
r
Vtune
D1
D3
D4
D2
5.0 GHz
r
3.3 GHz
6 GHz4 GHz
(1 V)
3 GHz
Comparison of oscillation points
28
r15 GHz
20 GHz
Oscillator Case Study #1
Point of oscillation in this region.
Point of oscillation in this region.
Oscillator Case Study #2
(a) |Γd| = 1.4(b) |Γd| = 2(c) |Γd| = 4 versus the device reflection
coefficient angle.(d) is the oscillator Q for |Γd| = 2.
Required angle of device
29
rY = G +jBrr dY = G +jBdd
DeviceTank
Gd
Con
duct
ance
G
Amplitude A
r
Want high RP = 1/Gr so Gr is small.
RP = 1/Gr
Summary oscillation conditions
30
r
d
d
d
dd
Voltage controlled oscillatorSignificant resonator loss (due to varactor diodes)
3. Condition for oscillator start‐up (for a VCO with a lossy resonator).
0 0,
0d dr r
V V
G BB GV V
1. Kurokawa condition for stable single-frequency oscillation:
2. Simplified Kurokawa condition (easy to design to):
0 0,
0d r
V V
G BV
Require that ( ∂Bd /∂V = 0) and ( ∂Gr /∂ω = 0). (If lossy resonator.)
Case Study Osc2: Part CResonator Design
Slides copyright 2013 M. Steer.31
rY = G +jBrr dY = G +jBdd
DeviceTank
d rG G d rB B
At oscillation
Vtune
D1
D3
D4
D2
Kurokawa oscillator condition simplification
0 0,
0d dr r
V V
G BB GV V
Kurokawa condition for stable single-frequency oscillation:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
32
0 0,
0d r
V V
G BV
Kurokawa condition for simplified design:
0dBV
0rG
So, ideally want
and
-B
Amplitude
d
Also want
Br
Gd
G
Amplitude
r
andKeeps phase noise low as oscillation frequency does not depend on amplitude.
dGV
rB
is +ve so
must be +ve
Γr Γd
Resonator characteristic
rY = G +jBrr dY = G +jBdd
DeviceTank
V
33
0rG
So,
r
Increasing frequency
Con
duct
ance
G
Amplitude A
r
Also
B r
Line of constant conductance
No dependence on amplitude
rB
must be +ve
Γr ΓdResonator characteristic
rY = G +jBrr dY = G +jBdd
DeviceTank
V
34
Oscillator start‐up.
r
Γr Γd
Also tunable, must be able to rotate r by varying a tuning voltage.
Resonator design
r
35
LB
CBCR LR
chokeLVtune
2. LR and CR result in high rB
and can control magnitude.3. GR comes from LR (transmission line) and CR (varactor).
4. Dependence of Gr and Br on amplitude comes from varactor.
1. Keep resonator as a simple parallel LC circuit.
3. But a good resonator will have a large RF voltage swing.4. Make sure Vtune minimizes current flow.
2. Minimize current flow and Gr.
RF signal.
What if RF voltage swing is too large?
0dBV
Recall that we want
Vtune
D
Varactor stack reduces
38
V
Cj
−Vtune
RF signal.
RF signal.
0rBV
Vtune
D1
D3
D4
D2
V
Ceff
−4Vtune
RF signal.
RF
RF signal.
Vtune
Varactor stack reduces and
39
V
Cj
−Vtune
rG
Vtune
rGV
I0
VB
I
V
VI+
V
Ceff
−Vtune RF 4RF
RFI0
4VB
I
VRF
Greater tuning range since high current regions can be avoided.
Vtune
Varactor stack increases tuning range
40
V
Cj
−Vtune
Vtune
I0
VB
I
V
VI+
V
Ceff
−Vtune RF 4RF
RFI0
4VB
I
VRF
Greater tuning range since high current regions can be avoided.
Final resonator
r
Vtune
D1
D3
D4
D2
Adjustable short circuit
41
Adjustments
r
Vtune
D1
D3
D4
D2
A
B
C
A
C
B
Provide impedance transformation.
RF chokes
DC block
Capacitance adjustment (also DC block)
Model
TL
TL
42
4.8 GHz
5.0 GHz
4.6 GHz
4.5 GHz
r (1 V)
4.5 GHzr (3 V)r (1 V)
4.9 GHz4.6 GHz
4.4 GHz
4.3 GHz
4.2 GHz
4.7 GHz
Legend4.5 GHz
4.7 GHz
3.7 GHz
3 GHz
6 GHz3 GHz
3.3 GHz
6 GHz
4.5 GHz
r (3 V)
Reflection coefficient of the resonator at different biases
(x)
(x)
r
Vtune
D1
D3
D4
D2
If crossover of r and 1/dis as shown by
then changing the tuning voltage from 1 V to 3 V changes the oscilaltionfrequency from 4.5 GHz to 4.8 GHz.
43
(x)
(x)
r
Vtune
D1
D3
D4
D2
Summary: final resonator network
● Transmission line reduces loss compared to an inductor
● Varactor stack reduces resonator conductance.
● Varactor stack reduces dependence of resonator admittance on signal amplitude.
● Adjustments provided by A, B and C
● B fixed after layout
TL1
AB
C
44
Case Study Osc2: Part DActive Network Design
Slides copyright 2013 M. Steer.45
rY = G +jBrr dY = G +jBdd
DeviceTank
d rG G d rB B
At oscillation
d
Vout ZL Vcc
Reflection oscillator operation
One‐port oscillator
As the amplitude of the oscillation increases, the magnitude of the device conductance, |Gd|decreases while the conductance of the tank circuit, Gr is constant.
As the frequency of the oscillation increases the susceptance of the tank circuit, Br, changes while, Bd (ideally) does not change.
rY = G +jBrr dY = G +jBdd
DeviceTank Bd
Sus
cept
ance
Frequency, f
rB
Gd
Con
duct
ance
G
Amplitude A
r
46
LBRL
CBCR LR
chokeLOutputVtune
Ideal
Ideal
Active network operation
One‐port oscillator
Keep Gd independent of amplitude to reduce phase noise.
Curve (a) is simple ideal response, curve (b) response is even better.rY = G +jBrr dY = G +jBdd
DeviceTank Bd
Frequency, f
rB
Gd
B
Amplitude A
d
47
LBRL
CB
Output
(b)
(a)
(x)
Active networkResonator network
50
47.5
2k
47.5
TL 1
(x)
10pF
2.2nH
10pF2.2pF
3.6nH
8.2nH
8.2nH
8.2nH
0.5pF 0.5pF
10pF
10pF
8.2nHCHOKEL
Ca Cb
VoutZL
V tune
D1
D3
D4
D2
VccI cc
Active network
d
(x)
(x)
Vout ZL Vcc
Ca Cb
RF SHORT
RF SHORT
Ca and Cb adjust d so that and d ( f )
is parallel to r ( f ).
0dBV
RF SHORT
Ideal
RF OPEN
LBRL
CBLR
Output
The resistors are required for biasing.
48
Kurokawa oscillator condition
0 0,
0d r
V V
G BV
Kurokawa condition for simplified design:
rY = G +jBrr dY = G +jBdd
DeviceTank
V
r
d
d
d
dd
Γr Γd
0dBV
and 0dG
49
Design device circuit so that
Oscillation startup
Small and large signal 1/d
0dBV
0dG
50
r
d
d
d
dd
Want 1.
(low phase noise)
3. (uniform amplitude of oscillation across tuning range )
2.
Large |Gd| at small signal levels. (|1/d| is small at a small signal level).
(fast start up of oscillation)
Increasing frequency
Increasing amplitude
Simulated reflection coefficient of the resonator, Γr, and the inverse of the small‐signal reflection coefficient of the active device, 1/Γd, of the C‐band VCO for various values of the compensation capacitors Ca and Cb.
Simulated reflection coefficient of the resonator, Γr, and the inverse of the small‐signal reflection coefficient of the active circuit, 1/Γd, with Ca = 0.5 pF and without Cb.
d1/3 GHz
d1/6 GHz
5.0 GHz
Increasing
level
6 GHz
r(3 V)
4 GHz
3 GHz
3.7 GHz
Multiple crossings
d
Vout ZL Vcc
Ca Cb
53d1/
3 GHz
d1/6 GHz
5.0 GHz
Increasing
level
6 GHz
r(3 V)
4 GHz
3 GHz
3.7 GHz
Multiple simultaneous oscillation
Measured
54
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.
Active network
55
d
Vout ZL Vcc
Summary: active network design
d
Vout ZL Vcc
CaCb
d
Vout ZL
Vcc
Ca Cb
RF OPEN
Circuit at RF:
● Active network needs to be optimized using measurements (cannot model sufficiently).
● Ca and Cb enable shaping of 1/d
● Need to avoid multi oscillation.
● Need Gd independent of frequency. (Constant amplitude oscillation.)
● Need large | Gd | for fast startup.
56
Case Study Osc2: Part EFinal Iteration on VCO Design
Slides copyright 2013 M. Steer.57
(a)
(b)
(c)
(x)
Active networkResonator network
d
(x)
(x)
L
Vout ZL Vcc
(x)
(x)
r
V tune
D1
D3
D4
D2
50
47.5
2k
47.5
TL 1
(x)
10pF
2.2nH
10pF2.2pF
3.6nH
8.2nH
8.2nH
8.2nH
0.5pF 0.5pF
10pF
10pF
8.2nHCHOKEL
Ca Cb
VoutZL
V tune
D1
D3
D4
D2
VccI cc
VCO schematic
58
Adjustable features
Final VCO circuit
Active network
Resonator network
Adjustable features 59
Resonator and active device circuits.
60
Active network
Resonator 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.
Measurement of the active network
The period of a 5 GHz signal is 200 ps.
So the connector has an electrical length of 63o.
The reflection coefficient is rotated by 126o. So measurements must be corrected.
The SMA connector also has parasitic capacitance and inductance. Correction will not be perfect.
61
Measured Γr at 3 V. r
3.8 GHz
3 GHz
6 GHz
5.3 GHz
Resonatormeasurements
Actual measurements rotated by −126o
Corrected
Raw
62
Measured Γr at 3 V.
Ca = 0.5 pF and Cb = 0.
1/Γd moves to the right as the signal level increases.
The intersection of 1/Γd and Γrdetermines the oscillation frequency and the signal level.
d1/
r
3.8 GHz
4.4 GHz
4.8 GHz
5.4 GHz
3 GHz
3 GHz
6 GHz
Small signal
5.3 GHzMeasurement
d3 GHz
6 GHz
5.0 GHz
Increasing
level
6 GHz4 GHz
3 GHz
3.7 GHz
Comparison
Measured
64
d
r
3.8 GHz
4.4 GHz
4.8 GHz
5.4 GHz
3 GHz
3 GHz
6 GHz
5.3 GHz
Simulated
Ca = 0.5 pF and Cb = 0. Vtune = 3 V Small signal
r
0.4 S2.5
Simulation and measurement accuracy
● 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.
Simulation fidelity Measurement fidelity
65
Γr for 0V (curve a)to 9 V (curve g)
Large signal 1/Γd.
r
d
3.5 GHz
4.5 GHz
3 GHz
6 GHz
3 GHz
f
a
bcd
ge
6 GHz
5.3 GHz
4.8 GHz
5.3 GHz
Locus of oscillationLarge signal10 dBm
RR
RR
4.5 GHz
Large signal characteristic
66
(x)
(x)
r
D1
D3
D4
D2
Resonator adjustments
● Adjustments provided by A, and C
TL1
A
C
67
C
A
Active network adjustments
d
Vout ZL
Vcc
Ca Cb
Circuit at RF:
● Ca and Cb enable shaping of 1/d
68
CaCb
Measured tuning curve
69
At Vout (before the bandpass filter) indicating low‐level harmonic content.
Measured output power and harmonics
70
Phase noise measured
71
Summary: C band (5 GHz) VCO● 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.
