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1 September 2008 2006 by Fabian Kung Wai Lee 1 10 - High Power Circuits 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. September 2008 2006 by Fabian Kung Wai Lee 2 References [1]* G. Gonzalez, “Microwave transistor amplifiers - analysis and design”, 2nd Edition 1997, Prentice-Hall. [2] C. W. Sayre, “Complete wireless design”, 2001, McGraw-Hill. [3]* S. C. Cripps, “RF power amplifier for wireless communications”, 1999, Artech House (2 nd edition 2005 is available). [4] G. D. Vendelin, A. M. Pavio, U. L. Rohde, “Microwave circuit design - using linear and nonlinear techniques”, 1990, John-Wiley & Sons (2 nd edition 2005 is available). [5] S. A. Maas, “Nonlinear microwave circuits”, 1988, Artech House. [6] G. Massobrio, P. Antognetti, “Semiconductor device modeling with SPICE”, 2nd edition, 1993, McGraw-Hill. [7]* B. Razavi, “RF microelectronics”, 1998 Prentice Hall. [8] Gilmore R., Besser L., “Practical RF circuit design for modern wireless systems”, Vol. 1 & 2, 2003, Artech House. [9] Gray P. R., Meyer R. G., “Analysis and design of analog integrated circuits”, 3rd Edition, 1993, John-Wiley & Sons.

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Page 1: Oscillator Design

1

September 2008 2006 by Fabian Kung Wai Lee 1

10 - High Power Circuits

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 informationpresented herein, and shall not be responsible for any errors, omissions or damagesas a result of the use of this information.

September 2008 2006 by Fabian Kung Wai Lee 2

References

• [1]* G. Gonzalez, “Microwave transistor amplifiers - analysis and design”, 2nd Edition 1997, Prentice-Hall.

• [2] C. W. Sayre, “Complete wireless design”, 2001, McGraw-Hill.• [3]* S. C. Cripps, “RF power amplifier for wireless communications”,

1999, Artech House (2nd edition 2005 is available).• [4] G. D. Vendelin, A. M. Pavio, U. L. Rohde, “Microwave circuit design

- using linear and nonlinear techniques”, 1990, John-Wiley & Sons (2nd

edition 2005 is available).• [5] S. A. Maas, “Nonlinear microwave circuits”, 1988, Artech House.• [6] G. Massobrio, P. Antognetti, “Semiconductor device modeling with

SPICE”, 2nd edition, 1993, McGraw-Hill.• [7]* B. Razavi, “RF microelectronics”, 1998 Prentice Hall.• [8] Gilmore R., Besser L., “Practical RF circuit design for modern

wireless systems”, Vol. 1 & 2, 2003, Artech House. • [9] Gray P. R., Meyer R. G., “Analysis and design of analog integrated

circuits”, 3rd Edition, 1993, John-Wiley & Sons.

Page 2: Oscillator Design

2

September 2008 2006 by Fabian Kung Wai Lee 3

1.0 Introduction

May 2009 2006 by Fabian Kung Wai Lee 4

Introduction

• Thus far we have considered various aspects of small-signal amplifier design based on small-signal S-parameters.

• The small-signal S-parameters are not useful for large-signal or high power circuit design such as power amplifier, mixers, frequency converters because the active devices (i.e. transistor/FET/diode) in these circuits usually operate in the nonlinear regions (recall that S-parameters are obtained by assuming the BJT or FET to be linear).

• In large-signal circuits the voltage and current variation will be large, for BJT this means the variation of the transistor terminal voltages will be greater than VT.

• Here we will concentrate on aspects of large-signal circuit design concerning power amplifiers and mixers .

• This short note will focus on discrete design, using BJT or FET, although the concepts can be extended to integrated circuit design.

Page 3: Oscillator Design

3

Small-Signal Versus Large-Signal Operation

• Consider a 2-port system:

September 2008 2006 by Fabian Kung Wai Lee 5

ZL

Vs

Zs

Large-signal

Small-signal

( ) ( ) ( ) ( ) ...33

221 TOHtvatvatvatv iiio +++=

f

Usually non-sinusoidal waveform

vi(t)

vo(t)

f

Sinusoidal waveform

T

1/T

September 2008 2006 by Fabian Kung Wai Lee 6

Large-Signal Model of Active Components (1)

• Amplitude of the voltage and current in the transistor/FET of high power circuit is large so that small-signal linear model (such as hybrid pi model) cannot be employed.

• We must use large-signal model of the transistor, such as Eber-Molls model, the Gummel-Poon model, the VBIC model. For MOSFET, the BSIM model is popular.

• Design of high power circuits is more of an art. A lot of experience is needed.

• Usually nonlinear circuit simulator is used (such as SPICE based circuit simulator). Simulation algorithms such as nonlinear transient simulation for time-domain and harmonic-balance (HB) method for frequency-domain are usually employed, see [5] for a primer into the HB method.

• The active device model is very important, as it affects the accuracy of the simulation result.

Page 4: Oscillator Design

4

September 2008 2006 by Fabian Kung Wai Lee 7

Large-Signal Model of Active Components (2)

• Most bipolar junction transistor and field effect transistor manufacturers provide SPICE based model of their device online, these are usually Gummel-Poon model or VBIC model for BJT and BSIM model for FET.

• These models usually come in the form of a netlist of a sub-circuits, which we can easily incorporate into our schematic using commercial circuit simulators.

• Here a design example of Class A power amplifier will be shown. This can also be applied to Class AB and Class B. Class C, E, F and others will not be discussed in depth due to lack of time.

• Please refer to Cripps [3] for more details.

September 2008 2006 by Fabian Kung Wai Lee 8

Large-Signal Model for Bipolar Junction Transistor (BJT)

CC

CE

rB

rC

rE

VBC

VBE

B

E

C

R

ECI

β

F

CCI

βLEI

LCI

ECCC II −

As an example see http://www.designers-guide.org/Modeling/ and eesof.tm.agilent.com/docs/iccap2002/ MDLGBOOK/7DEVICE_MODELING/3TRANSISTORS/2VBICfor more information on VBIC models.

• The most popular large-signal model for BJT is the SPICE Gummel-Poon(SGP) model (See Ref [6] for further details). A more recent alternative to the SGP model is the Vertical Bipolar Intercompany Model (VBIC) model which offers more accuracies as compared to SGP model.

• The SPICE Gummel-Poon model is based on the device physics of bipolar junction transistor. A simplified version is shown below.

C

B

E

Page 5: Oscillator Design

5

September 2008 2006 by Fabian Kung Wai Lee 9

Relationship Between Large and Small-Signal Models

IC

VCE0IB1

IB2

IB3

IB4

IB5

D.C. load line

Small-signal model

Large-signal model

CC

CE

rB

rC

rE

VBC

VBE

B

E

C

R

ECI

β

F

CCI

βLEI

LCI

ECCC II −

September 2008 2006 by Fabian Kung Wai Lee 10

Large-Signal Model for MOS Field Effect Transistor (1)

• For MOSFET, the current industry standard is the BSIM (Berkeley Short-channel IGFET Model, IG stands for insulated-gate) model.

• BSIM is a physics-based threshold model of field-effect transistor. It is accurate, scalable, robust and predictive MOSFET SPICE model for circuit simulation and CMOS technology development. It is developed by the BSIM Research Group in the Department of Electrical Engineering and Computer Sciences (EECS) at the University of California, Berkeley.

• Optimized for modeling MOSFET in VLSI circuits, deep submicron technology (<0.25µm channel length).

• Various flavors (in the order of increased complexities and accurracy) e.g. BSIM1, BSIM2, BSIM3, BSIM4 and BSIMSOI.

• Official homepage: http://www-device.eecs.berkeley.edu/~bsim3/• See Massobrio & Antognetti [6] for more information on large signal

field effect transistor modeling.

Page 6: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 11

Large-Signal Model for MOS Field Effect Transistor (2)

• SPICE model for NMOS field-effect transistor.

CGD

ECCC II −

G

D

S

BCGS

CGB

CDB

CSB

RD

RS

iD

DDB

DSB

G

D

S

B

PN+

S G D

N+P+

B

SiO2

Silicon substrate(semi-insulating)

September 2008 2006 by Fabian Kung Wai Lee 12

Large-Signal Model for MOS Field Effect Transistor (3)

• In recent year there is an alternative to BSIM, based on physics-based surface potential or inversion charge based model.

• This model is called PSP MOSFET model and is jointly developed by Pennsylvania State University and Philips Semiconductor. PSP probably stands for (Pennsylvania or Philips Surface Potential).

• The PSP model includes an accurate description of all physical effects important for modern and future CMOS technologies.

• See http://www.semiconductors.philips.com/Philips_Models/mos_models/psp/ and http://pspmodel.ee.psu.edu/introductiontopsp.asp for more information.

Page 7: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 13

2.0 Basic Power Amplifier Design

September 2008 2006 by Fabian Kung Wai Lee 14

Amplifier Classification (1)

• According to signal level:

– Small-Signal Amplifier.

– Power Amplifier (Large-Signal Amplifier).

• According to dc biasing scheme:

– Class A.

– Class B.

– Class AB.

– Class C.

Almost all small-signal amplifiers are Class A

Page 8: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 15

Amplifier Classification (2)

VCE

Rc

Vcc

VCE

IC

Rc

Vcc

VCE

IC

Re

IC

IB=0

D.C. load line

Class A

Class AB

Class B

Class C

cCCEcc RIVV +=

( )ecCCEcc RRIVV ++=

D.C. LoadLine equation

or

September 2008 2006 by Fabian Kung Wai Lee 16

Important Parameters for Power Amplifier

• Maximum output power.• Efficiency (%).• Harmonic Distortion or Linearity.• Large-signal power gain (dB) / maximum power rating (W).• Operating voltage (V).

• Bandwidth (Hz).

• Isolation.

Page 9: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 17

Class-A Power Amplifier Schematic Template

Vcc

Rb1

Rb2Re

Cc1

Cc2

Ce

L1

L2

L3

Cd

OutputMatchingNetwork

InputMatchingNetwork RL

t

vb

t

vc

• Low efficiency (<50%).• High linearity.• Suitable for wideband system.• Suitable for low voltage system.

Note that most poweramplifiers are of CE orCC configurations.

September 2008 2006 by Fabian Kung Wai Lee 18

Class-B Power Amplifier Schematic Template (Push-Pull Configuration)

Vcc

Rb

Cc1 Cc2

L1

L2

Cd

OutputMatchingNetwork

InputMatchingNetwork

RL

Rb

D1

D2

t

v

b

t

ic

t

-ic• High efficiency (<78%).• High linearity.• Suitable for wideband system.• Need higher operating voltage.

The active device is onlyactive half the time, or 180o

Page 10: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 19

Class-C Power Amplifier Schematic Template

Vcc

Rb

Cc1

Cc2L1

L2

Cd

OutputMatchingNetwork/Band-passFilter

InputMatchingNetwork RL

Can also connect tonegative supply

t

v

b

t

ic

f

f

• High efficiency (<90%).• Poor linearity.• Suitable for narrowband system.• Suitable for low voltage system.

The active device is onlyactive less than half the time, or <180o

A Short Summary on Other Classes

• Class F Amplifier – The Class F amplifier is a special variant of Class B. This class of amplifier achieves even higher efficiency than Class B by reactively tune the harmonics to ensure no dissipation at harmonic frequencies and also to minimize power dissipation by keeping the active device voltage as low as possible when the current is high.

• Class E Amplifier (Switching Amplifier) – Class E amplifier is similar to the Class B or F in that the active device is normally driven with a 180o

conduction angle between saturation and cut-off. However it uses a switching principle so that any analog relationship between the input and output is lost.

• Class D Amplifier (Switching Amplifier) – Class D amplifier utilizes the switching principle by driving two active devices in tandem, to ensure that when one device is conducting the other device is forced off. It can be regarded as a push-pull Class F amplifier.

September 2008 2006 by Fabian Kung Wai Lee 20

Page 11: Oscillator Design

11

Amplifier Large-Signal Response – 1 Tone Excitation (1)

• Consider an amplifier which can be characterized by a power series expansion of it’s input.

• If the input voltage is a sinusoidal signal (1 Tone), and considering up to 3rd order:

September 2008 2006 by Fabian Kung Wai Lee 21

( )tvo( )tvi

( ) ( ) ( ) ( ) ...33

221 TOHtvtvtvtv iiio +++= ααα

( ) ( )tAtvi ωcos=

( ) ( ) ( ) ( )tAtAtAtvo ωαωαωα 333

2221 coscoscos ++≅

( ) ( )[ ] ( ) ( )[ ][ ] ( ) ( ) ( )tAtAtAAA

ttAtAtA

ωαωαωαααωωαωαωα

3cos2coscos

3coscos32cos1cos3

3412

2212

343

12

221

334

1222

11

++++=

++++=

DC term Fundamental frequencyterm (Po)

1st harmonicterm (P1)

2nd harmonicterm (P2)

|Vi(f)|

f

|Vi(f)|

f

(2.2)

(2.1)( ) ( )( )12coscos 2

12 += θθ

( ) ( )( )θθθ 3coscos3cos 413 +=

Typically α3 is negative

Amplifier Large-Signal Response - 1 Tone Excitation (2)

• Now converting all powers into dB scale, assuming the system impedance is Zo (real) and we are referencing with respect to 1mW.

• Input power:

• Fundamental:

• Similarly we can show that:

• 1st harmonic:

• 2nd harmonic:

September 2008 2006 by Fabian Kung Wai Lee 22

22

1 APoZin = ( )001.0/log10 2_

2

oZA

dBminP =

( )[ ][ ] ( )1_

234

31_

2

2234

31_

log20log20

001.0/log102

ααα

αα

+≅++=

+=

dBmindBmin

ZA

dBmo

PAP

APo

Pin/1mW

( ) 30log102 222__1 −+= αoz

dBmindBm PP

( ) 60log203 32__2 −+= αozdBmindBm PP

Pin/dBm0

Slope=1

Slope=2

Slope=3

(2.3a)

(2.3b)

(2.3c)

(2.3d)

Active componentgoes into saturation

Page 12: Oscillator Design

12

September 2008 2006 by Fabian Kung Wai Lee 23

Amplifier Large-Signal Response - 2 Tones Excitation (1)

( ) ( ) ( ) ( ) ...33

221 TOHtvtvtvtv iiio +++= ααα

( ) ( ) ( )tAtAtvi 2211 coscos ωω +=( ) ( )( ) ( )

( ) ( )( ) ( )( ) ( )tt

tt

tAAtAA

tAAAA

tAAAA

AAAA

AAAA

1243

1243

12

2143

2143

21

212122121221

221232

33234

3212

122132

33134

3111

2cos2cos:2

2cos2cos:2

coscos:

cos:

cos:

12231

223

22132

213

ωωωωωω

ωωωωωω

ωωαωωαωωωαααω

ωαααω

αα

αα

−++±

−++±

−++±++

++

Component of interestin implementing mixercircuit

Component of interestin implementing amplifier

Undesirable components,cause IntermodulationDistortion (IMD).

ff1-f2

2f1-f2 2f2-f1

f2f1 2f1f1+f2 2f2

3f1 3f2

2f1+f2 2f2+f1

|Vo|

IMD

ff1 f2

|Vi|

2 sinusoidal signalAt f1 and f2

(2.4)

( )tvo( )tvi

(2.5a)

(2.5b)

(2.5c)

(2.5d)

(2.5e)

Note that we interchagef and ω freely

September 2008 2006 by Fabian Kung Wai Lee 24

Amplifier Large-Signal Response - 2 Tones Excitation (2)

• Let A1 = A2 = A, and α3 << α1.

• Now converting all powers into dB scale, assuming the system impedance is Zo (real) and we are referencing with respect to 1mW.

• As in 1 Tone excitation case, we again notice that:

– Fundamental Component : The output power at f1 and f2 (Po_f1, Po_f2) increases with slope = 1 with respect to Pin in dBm (for Pin sufficiently small).

– Mixing Component : The output power at f1-f2 and f1+ f2 increases with slope = 2 with respect to Pin in dBm.

– Intermodulation Component : The output power at 2f1±f2 and 2f2±f1increases with slope = 3 with respect to Pin in dBm.

( ) ( )tAA 12

349

11 cos: ωααω + ( ) 2212

122234

912

11_ AAAP

oo ZZo αααω ≅+=

( ) ( )tt AA214

3214

321 2cos2cos:2

33

33 ωωωωωω αα −++±

( )tA 212

221 cos: ωωαωω −−

( )2334

32

12_ 21

APoZo αωω =−

( )2222

1_ 21

APoZo αωω =−

Page 13: Oscillator Design

13

September 2008 2006 by Fabian Kung Wai Lee 25

Amplifier Large-Signal Response - 2 Tones Excitation (2)

• For amplifier design, Po_f1 , Po_ 2f1-f2 and Po_ 2f2-f1 (or related components) versus Pin are off interest. These can be plotted in dB scale are shown in the next slide.

• Po_ 2f1-f2 and Po_ 2f2-f1 are typically very close to the fundamental terms, thus are difficult to remove via band-pass filtering, and result in distorted output signals.

• For mixer design, Po_ f1±f2 versus Pin are off interest.

September 2008 2006 by Fabian Kung Wai Lee 26

Dynamic Range, 1dB Gain Compression and Third Order Intercept Point

• Plotting P2ω2-ω1, Pω1 versus Pin in log scale, a few parameters can be defined:

Pout

(dBm)

-20

-10

0

10

20

30

Noise Floor

-70 -60 -50 -40 -30 -20 -10 0 10

Pin

(dBm)20

-30

-40

-50

-60

Dynamic range (DR)

1dB compressionpoint (Pin_1dB)

Saturation

Burnout

Power gain Gp = Pout(dB) - Pin(dB)

1dB Gain compressionPoint

Spurious freedynamic range(DRf)

Third-order InterceptPoint (TOI)

1

1

1

3

Note : Spurious free dynamic range is important, for within this range the 3rd

order component power is less than the noise power, thusdistortion due to this component is negligible.

1ωP

122 ωω −P

PIP

Po,mds

P1dB

Page 14: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 27

Some Useful Relations for Large-Signal Parameters

• Please refer to Chapter 2 of [7] and Chapter 4 of [1] for derivation.

• All parameters are in dB scale.

dBPP dBIP 101 +≅IPPPP 23 1212 −=− ωωω

( )mdsoIPf PPDR ,32 −=

( )21211 23

22 ωωωωω −− −=− PPPP IP

Po/dBm

Pin/dBm

DRf

PIP

1ωP212 ωω −P

Po,mds

P1dB

≅10dB( )2111 222 ωωωω −−+= PPPPIP

IMDPPIP 21

1+=⇒ ω

211 2 ωωω −−= PPIMDwhere

(2.2a)

(2.2b)

(2.2c)

IMD

September 2008 2006 by Fabian Kung Wai Lee 28

Relationship between TOI, DR, DR f and Linearity (1)

• Levels of input and output TOI, DR and DRf indicate the linearity of the power amplifier.

• Highly linear power amplifier has small α2 and α3 compare to α1.

• Large DR implies small α2/ α1 ratio.

• Large DRf and TOI levels imply small α2/ α1 and α3/ α1 ratios.*

• In essence, a linear power amplifier

- Has larger DR and DRf.

- Has larger TOI levels.

*Here we ignore the effect ofhigher order terms (H.O.T.) andtime delay effect.

Undesirable, suppress these

( ) ( ) ( ) ( ) ...33

221 TOHtvtvtvtv iiio +++= ααα

Page 15: Oscillator Design

15

Relationship between TOI, DR, DR f and Linearity (2)

• The 1dB Gain Compression point (P1dB) and the TOI point (PIP) are important as both determine the dynamic range DR and the spurious-free dynamic range DRf.

• The DRf is usually taken as the output power range where the large-signal amplifier is considered linear.

September 2008 2006 by Fabian Kung Wai Lee 29

Po/dBm

Pin/dBm

1ωP

212 ωω −P

Po,mds

Smaller DRf (larger |α3|)

Larger DRf (smaller |α3|)

Suppose we have 2amplifiers, with differentα3 values. Typically |α3|<<1, so it’s logarithm is negative. One with larger |α3| (blue) and theother with smaller |α3| (red).

( ) ( ) ( ) 60log203 343

10_001.0log102

43

21

210

33

12−+ →=± αα

ωω odBmin

PAZ ZPP

o

Measuring TOI Level

• Equation (2.2b) provides a convenient way to measure the third-order intercept point (IP) output power PIP.

• A typical setup is shown below:

September 2008 2006 by Fabian Kung Wai Lee 30

CW Generator 1at f1

CW Generator 2at f2

Power Combiner

SpectrumAnalyzer

CW = Continuous sine WaveOutput power level for bothgenerators must be similar

Amplifierunder test

Note that cable and connectorloss has to be accounted for.

f1 f2 2f2-f12f1-f2f

Power/dBm

IMD

IMDPPIP 21

1+= ω

Note that the IMDlevel will decreaseas CW generatoroutput is increased.

Po

Pin

PIP

1ωP212 ωω −P

Page 16: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 31

For Class A, AB and B Power Amplifier- Constant P 1dB Contour

Typical Powercontour for FET at a fixed frequency.The power contour is obtainedby varying the loadimpedance whileensuring conjugatematch at the input, thenthe input power is slowlyincreased until1dB gain compressionis observed. ZL with similar P1B are thenjoint together. ΓL Plane

At fixed frequency !

P1dB Contour

September 2008 2006 by Fabian Kung Wai Lee 32

For Class A, AB and B Power Amplifier - Large-Signal Reflection Coefficients

Typical Γs and ΓL as a function of frequency for an FET amplifier

Large-signal Γs

Large-signal ΓL

Page 17: Oscillator Design

17

Large-Signal Parameters Measurement Setup

• A typical setup as shown below is used to obtain the large-signal data on the previous slides.

May 2009 2006 by Fabian Kung Wai Lee 33

PowerMeterA

PowerMeterB

PowerMeterC

A A

B B

Transistor AmplifierUnder Test

D.C.Supply

Load

SignalGenerator

Input tuningStub

Output tuningStub

For measuring theamount of mismatchat input

For measuringInput power

For measuringOutput power

VariableAttenuator

RF choke

Directionalcoupler

September 2008 2006 by Fabian Kung Wai Lee 34

Example 2.1 – Class-A Power Amplifier Design

• In this example we would like to design a single transistor Class-A power amplifier for a battery operated device at operating frequency fo = 868.0 MHz.

• The amplifier is driven by a source with 50Ω source impedance and with available power level of PA= -5.0 dBm or 0.32 mW. The output power into a 50Ω load is required to be 10.0 mW or 10 dBm.

• The transistor chosen for the job is BFG520 from Philips Semiconductors. This is an NPN wideband transistor, with fT = 9 GHz, IC(max) = 70 mA and maximum power dissipation of 300 mW. Using a transistor with fT > 5×fo allows us to reduce the dc collector current (IC), thereby reducing idle power dissipation.

• Here we rely on Agilent Technologies ADS 2003C software for the analysis.

Page 18: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 35

Example 2.1 - Class A Power Amplifier Design Cont…

• The basic amplifier core circuit.

• DC analysis is performed to find the transistor quiescent point.DC analysis results:Vcc = 3.3 VIc = 10.8 mAVCE = 2.14 VIdeal voltage swing = 2.14 V

3.30 V

811 mV

811 mV811 mV

811 mV

811 mV

811 mV

2.14 V

2.14 V 2.14 V

2.14 V

2.14 V

2.14 V2.14 V

2.14 V2.14 V

2.14 V

DCDC1

DC-11.6 mA

V_DCVCCVdc=3.3 V

811 uA

RRB2R=1 kOhm

PortP1Num=1

PortP2Num=2

10.7 mA

LL1

R=L=100.0 nH

0 ACCD1C=100.0 pF

0 ACCD2C=22.0 pF

74.9 uA10.7 mA

10.8 mA

-10.8 mA

pb_phl_BFG520_19921215Q174.9 uA L

LB

R=L=100.0 nH

885 uA

RRB1R=1.5 kOhm

11.6 mA

RRCR=100 Ohm

InputTerminal

OutputTerminal

mW0.38V3.3mA5.11 =⋅== ccccdc VIP

%3.26100 )( Efficiency lTheoretica3810 =×=η

%5.25100 (PAE)

Efficiency AddedPower lTheoretica

3832.010 =×= −

This is within the limitof ideal efficiency of 50% for Class-A PA

A compromise hasto be made in termsof voltage swingand IC, owing to thedc biasing circuit chosen.

September 2008 2006 by Fabian Kung Wai Lee 36

Example 2.1 – Class-A Power Amplifier Design Cont…

• Performing a load pull test to find the optimum load impedance ZL.

VSupply

Vin

NOTE: Depending on the v alue of the internal v ariable 'f req', the v ariable TLArray Index will assume the integerv alue 0 if f req = dc, 1 if f req = f undamental,2 if f req = 1st harmonic etc. This prov idesthe index to the one dimensional arrayTLArray [ ]. Thus ef f ectiv ely the HarmonicBalance solv er will 'see' dif f erent load impedance/ref lection coef f icient at dif f erentf requencies. Similar action is perf ormed f or Source_Impedance Variable Equation.

This def ines the load andsource impedance at thef undamental and harnomics.Here we assume the circuitparasitics will short out thehigher harmonics

User can change theparameters in the Variable Equation"Stimulus_User_Setting"

VL

VARLoad_Ref lection_Coef f ient

TLoad=TLArray [TLArray Index]TLArray =list(r(ZL_dc),TL,r(ZL_2),r(ZL_3),r(ZL_4),r(ZL_5),r(ZL_6),r(ZL_7))TLArray Index=int(min(abs(f req)/RFf req + 1.5, length(TLArray )))

EqnVar

V_DCVccVdc=3.3 V

ParamSweepSweep1

Step=5Stop=360Start=0SimInstanceName[6]=SimInstanceName[5]=SimInstanceName[4]=SimInstanceName[3]=SimInstanceName[2]=SimInstanceName[1]="HB1"SweepVar="TLphase"

PARAMETER SWEEPVARStimulus_User_Settings

Ps_dBm=-5Max_Rho=0.9Max_Harmonic=5RFf req=868 MHzZo=50

EqnVar

HarmonicBalanceHB1

Step=0.1Stop=Max_RhoStart=0SweepVar="TLmag"Order[1]=Max_HarmonicFreq[1]=RFf req

HARMONIC BALANCE

VARSource_Impedance

Zs=ZsArray [ZsArray Index]ZsArray =list(Zs_dc,Zs_1,Zs_2,Zs_3,Zs_4,Zs_5,Zs_6,Zs_7)ZsArray Index=int(min(abs(f req)/RFf req + 1.5, length(TLArray )))

EqnVar

VARLoad_Ref lection_Coef f icient_Sweep

TL=TLcenter+TLmag*exp(j*(TLphase/180)*pi)TLcenter=0r(x)=(x-Zo)/(x+Zo)TLphase=0TLmag=0

EqnVar

VARLoad_Source_Impedance_at_Harmonics

Zs_7=1+j*0Zs_6=1+j*0Zs_5=1+j*0Zs_4=1+j*0Zs_3=1+j*0Zs_2=1+j*0Zs_1=ZoZs_dc=ZoZL_7=1+j*0ZL_6=1+j*0ZL_5=1+j*0ZL_4=1+j*0ZL_3=1+j*0ZL_2=1+j*0ZL_dc=1000000

EqnVar

P_1TonePORT1

Freq=RFf reqP=polar(dbmtow(Ps_dBm),0)Z=Zs OhmNum=1

PA_coreX1

I_ProbeISupply

I_ProbeISource

I_ProbeILoad S1P_Eqn

S1P1

Z[1]=ZoS[1,1]=TLoad

CCc1C=100.0 pF

CCc2C=100.0 pF

NonlinearHB analysisis applied. Thisis a single-toneanalysis since thereis only one source.Up to 5th harmonicis considered.(Max_Harmonic = 5)

one tonesource(at 868 MHz)PA = Ps_dBmor -5 dBm inthis instance.

Amplifier corecircuit (see previousslide)

Expressions to set theload and source impedance at theharmonics.

Expression to sweep ΓL acrossthe Smith Chartin polar form.

Expressions to generate the correctΓL and Zs at each frequency component during HB analysis

Source availablepower = -5dBminto 50Ω load.

Page 19: Oscillator Design

19

September 2008 2006 by Fabian Kung Wai Lee 37

Example 2.1 – Class-A Power Amplifier Design Cont…

• Method of sweeping ΓL to cover the Smith Chart.

• Sweeping theangle of ΓL from 0 to 360o,at 5o interval andthe magnitude |ΓL|from 0 to 0.9 at 0.1step. • Of course wecould refine thisby using smaller steps at the expenseof greater computationalresources needed.

θ|Γ|

Re Γ

Im Γ

September 2008 2006 by Fabian Kung Wai Lee 38

Example 2.1 – Class-A Power Amplifier Design Cont…

• The expressions on the ADS’s Data Display required to generate a contour plot of load power PL at fundamental frequency on the Smith Chart.

Eqn PL1_watt = re(0.5*VL[::,::,1]*conj(ILoad.i[::,::,1]))

Eqn PL1_dBm = 10*log10(PL1_watt) + 30

Eqn PL1_dBm_max = max(max(PL1_dBm))

Eqn PL_step = 0.2

Eqn NumLine = 6

Eqn contour_PL1_dBm = contour(PL1_dBm, PL1_dBm_max-0.01-[0::NumLine-1]*PL_step)

Eqn contour_PL1_dBm_polar = indep(contour_PL1_dBm)*exp(i*(contour_PL1_dBm/180)*pi)

PL1_dBm_max9.151

Create a contour plot for load power. This actually produces a 3D array. The indexes to thearray corresponds to 1) the Power 2) TLmag and 3) TLphase. This can be plotted on X-Y plotwhere TLmag forms the x-axis, and TLphase forms the y-axis.

Change the contour plot into polar form. The function indep( ) returns the independent variableassociated with the datatype contour_PL1_dBm. There are two independent variables associatedwith contour_PL_dBm, since we varies the magnitude and phase of TL. The innermost independentvariable is TLmag, since it is embedded in the Harmonic Balance simulation control. So this isreturned by the indep( ) function. Datatype contour_PL1_dBm itself is simply the phase in degrees. So this can be easily converted in polar form.

Compute Load power and Creating Load Power ContourVL[::,::,1] extracts the fundamental component of the load voltage, for all (as indicated by the symbol '::') TLmag and TLphase. Same can be said for ILoad.i[::,::,1]

Eqn Distortion_step = 0.05

Eqn N_step = 3

Maximum loadpower (9.151 dBm) at fundamentalfrequency, with inputpower -5 dBm into 50Ω load, inputnot match condition.

freqTLphase=0.000, TLmag=0.000

0.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

TLphase=0.000, TLmag=0.1000.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

TLphase=0.000, TLmag=0.2000.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

Mix

012345

012345

012345

Note: Plotting out the variable ‘Mix’ in the Data Display shows the index to the frequency components

Page 20: Oscillator Design

20

September 2008 2006 by Fabian Kung Wai Lee 39

Example 2.1 – Class-A Power Amplifier Design Cont…

• The expressions on the ADS’s Data Display required to generate a contour plot of total load power PL at the harmonics and Efficiency on the Smith Chart.

Eqn PL2_watt=re(0.5*VL[::,::,2]*conj(ILoad.i[::,::,2]))

Eqn PL3_watt=re(0.5*VL[::,::,3]*conj(ILoad.i[::,::,3]))

Eqn PL4_watt=re(0.5*VL[::,::,4]*conj(ILoad.i[::,::,4]))

Eqn PL5_watt=re(0.5*VL[::,::,5]*conj(ILoad.i[::,::,5]))

Eqn PL_harmonic_watt = PL2_watt + PL3_watt + PL4_watt + PL5_watt

Eqn Distortion_Ratio = PL_harmonic_watt/PL1_watt

Eqn Distortion_max = max(max(Distortion_Ratio))

Distortion_max0.212

Eqn contour_DR=contour(Distortion_Ratio, Distortion_max-0.05-[0::NumLine-1]*Distortion_step)

Eqn contour_DR_polar=indep(contour_DR)*exp(i*(contour_DR/180)*pi)

Eqn Pdc_watt = re(VSupply[::,::,0]*ISupply.i[::,::,0])

Eqn N = ((PL1_watt-Pin_watt)/Pdc_watt)*100

Eqn Nmax = max(max(N))

Eqn contour_N=contour(N,Nmax - 0.1-[0::NumLine-1]*N_step)

Eqn contour_N_polar = indep(contour_N)*exp(j*(contour_N/180)*pi)

Compute Harmonic Power and Creating the Harmonic Distortion Contour

Nmax20.259

Computing the Efficiency and Creating the Efficiency Contour

Eqn Pin_watt = 0.5*re(Vin[::,::,1]*ISource.i[::,::,1])

MaximumTotal Harmonic Distortion(ratio of 0.212)

MaximumEfficiency(20.259 %)

September 2008 2006 by Fabian Kung Wai Lee 40

Example 2.1 – Class-A Power Amplifier Design Cont…

• Superimposing the PL(at 868 MHz), Efficiency η and Total Harmonic Distortion Ratio contours on the Smith Chart.

m1TLmag=m1=0.357 / 45.000level=9.140921, number=1impedance = Z0 * (1.402 + j0.811)

0.357

m2TLmag=m2=0.440 / 110.000level=0.012150, number=2impedance = Z0 * (0.540 + j0.553)

0.440

TLmag (0.073 to 0.687)

con

tou

r_P

L1

_d

Bm

_po

lar m1

TLmag (0.375 to 0.900)

con

tou

r_D

R_p

ola

r

m2

TLmag (0.053 to 0.900)

con

tou

r_N

_p

ola

r

Point of max PL (9.14 dBm), ZLopt

Point of max Efficiency (20.26%)

• PL(868 MHz) step = 0.2 dBm• Efficiency (N) step = 3%• Harmonic Distortion

Ratio step = 0.05

From the plot:ZLopt = 70.1+j40.55at 868 MHz, and closeto 0 at harmonics.

We observe thatZL needed for highestoutput power and highestefficiency are similar, thuswe choose ZLopt to be givenby the PL(868MHz) contour

Page 21: Oscillator Design

21

September 2008 2006 by Fabian Kung Wai Lee 41

Example 2.1 – Class-A Power Amplifier Design Cont…

• The output transformation network design, approximated to standard L and C values.

VLVin

RRLR=50 Ohm

I_ProbeI_in

ACAC1

Step=5.0 MHzStop=4.0 GHzStart=0.1 GHz

AC

CC1BC=0.47 pF

LL1

R=L=8.2 nH

CC2C=8.2 pF

CC1AC=4.7 pF

V_ACSRC1

Freq=freqVac=polar(1,0) V

0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 3.4 3.6 3.80.0 4.0

-100

-80

-60

-40

-20

0

20

40

60

80

100

120

140

-120

160

freq, GHz

real

(Zin

)im

ag(Z

in)

A low-pass pi network,to suppress the harmonics.

Eqn Zin = Vin/I_in.i

Real part of Zin

Imaginary part of Zin

Narrowbandtransformation

September 2008 2006 by Fabian Kung Wai Lee 42

Example 2.1 – Class-A Power Amplifier Design Cont…

• After connecting the load network, we ‘measure’ the large-signal input impedance Zin at the fo of 868 MHz.

• We then design a low-pass impedance transformation network that transforms 50Ω Zs into Zin

* at fo = 868 MHz.

This defines the load andsource impedance at thefundamental and harnomics.Here we assume the circuitparasitics will short out thehigher harmonics

Vin VL

User can change theparameters in the Variable Equation"Stimulus_User_Setting"

VSupply

VARSource_Impedance

Zs=ZsArray[ZsArrayIndex]ZsArray=list(Zs_dc,Zs_1,Zs_2,Zs_3,Zs_4,Zs_5,Zs_6,Zs_7)ZsArrayIndex=int(min(abs(freq)/RFfreq + 1.5, length(TLArray)))

EqnVar

VARLoad_Source_Impedance_at_Harmonics

Zs_7=1+j*0Zs_6=1+j*0Zs_5=1+j*0Zs_4=1+j*0Zs_3=1+j*0Zs_2=1+j*0Zs_1=ZoZs_dc=ZoZL_7=1+j*0ZL_6=1+j*0ZL_5=1+j*0ZL_4=1+j*0ZL_3=1+j*0ZL_2=1+j*0ZL_dc=1000000

EqnVar

VARLoad_Reflection_Coefficient_Sweep

TL=TLcenter+TLmag*exp(j*(TLphase/180)*pi)TLcenter=0r(x)=(x-Zo)/(x+Zo)TLphase=0TLmag=0

EqnVar

VARLoad_Reflection_Coeffient

TLoad=TLArray[TLArrayIndex]TLArray=list(r(ZL_dc),TL,r(ZL_2),r(ZL_3),r(ZL_4),r(ZL_5),r(ZL_6),r(ZL_7))TLArrayIndex=int(min(abs(freq)/RFfreq + 1.5, length(TLArray)))

EqnVar

I_ProbeISource

CC1BC=0.47 pF

CC1AC=4.7 pF

LL1

R=L=8.2 nH

CC2C=8.2 pF

RRLR=50 Ohm

VARStimulus_User_Settings

Ps_dBm=-5Max_Rho=0.9Max_Harmonic=5RFfreq=868 MHzZo=50

EqnVar

HarmonicBalanceHB1

Step=Stop=Start=SweepVar=Order[1]=Max_HarmonicFreq[1]=RFfreq

HARMONIC BALANCE

V_DCVccVdc=3.3 V

P_1TonePORT1

Freq=RFfreqP=polar(dbmtow(Ps_dBm),0)Z=Zs OhmNum=1

PA_coreX1

I_ProbeISupply

CCc1C=100.0 pF

CCc2C=100.0 pF

Eqn Zin = Vin/ISource.i

freq0.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

Zin<invalid>

10.838 - j12.335-1.000 + j0.000-1.000 + j0.000-1.000 + j0.000-1.000 + j0.000

Eqn Zin = Vin/ISource.i

freq0.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

Zin<invalid>

10.838 - j12.335-1.000 + j0.000-1.000 + j0.000-1.000 + j0.000-1.000 + j0.000

The results:

Zin

Large-signalZin at fo = 868 MHz

Page 22: Oscillator Design

22

September 2008 2006 by Fabian Kung Wai Lee 43

Example 2.1 – Class-A Power Amplifier Design Cont…

• Finally, upon adding the input and output transformation networks.

• Note that we are performing conjugate matching at the input.

This defines the load andsource impedance at thefundamental and harnomics.Here we assume the circuitparasitics will short out thehigher harmonics

User can change theparameters in the Variable Equation"Stimulus_User_Setting"

Vin

VL

VSupply

VARLoad_Reflection_Coeffient

TLoad=TLArray[TLArrayIndex]TLArray=list(r(ZL_dc),TL,r(ZL_2),r(ZL_3),r(ZL_4),r(ZL_5),r(ZL_6),r(ZL_7))TLArrayIndex=int(min(abs(freq)/RFfreq + 1.5, length(TLArray)))

EqnVar

VARLoad_Reflection_Coefficient_Sweep

TL=TLcenter+TLmag*exp(j*(TLphase/180)*pi)TLcenter=0r(x)=(x-Zo)/(x+Zo)TLphase=0TLmag=0

EqnVar

VARLoad_Source_Impedance_at_Harmonics

Zs_7=1+j*0Zs_6=1+j*0Zs_5=1+j*0Zs_4=1+j*0Zs_3=1+j*0Zs_2=1+j*0Zs_1=ZoZs_dc=ZoZL_7=1+j*0ZL_6=1+j*0ZL_5=1+j*0ZL_4=1+j*0ZL_3=1+j*0ZL_2=1+j*0ZL_dc=1000000

EqnVar

VARSource_Impedance

Zs=ZsArray[ZsArrayIndex]ZsArray=list(Zs_dc,Zs_1,Zs_2,Zs_3,Zs_4,Zs_5,Zs_6,Zs_7)ZsArrayIndex=int(min(abs(freq)/RFfreq + 1.5, length(TLArray)))

EqnVar

VARStimulus_User_Settings

Ps_dBm=-5Max_Rho=0.9Max_Harmonic=5RFfreq=868 MHzZo=50

EqnVar

HarmonicBalanceHB1

Step=Stop=Start=SweepVar=Order[1]=Max_HarmonicFreq[1]=RFfreq

HARMONIC BALANCE

CC3C=5.6 pF

CC4BC=0.68 pF

CC4AC=10.0 pF

LL2

R=L=4.7 nH

P_1TonePORT1

Freq=RFfreqP=polar(dbmtow(Ps_dBm),0)Z=Zs OhmNum=1

I_ProbeISource

CC1BC=0.47 pF

CC1AC=4.7 pF

LL1

R=L=8.2 nH

CC2C=8.2 pF

RRLR=50 Ohm

V_DCVccVdc=3.3 V

PA_coreX1

I_ProbeISupply

CCc1C=100.0 pF

CCc2C=100.0 pF

Inputtransformationnetwork

Outputtransformationnetwork

Zin*

Zin

ZLopt

September 2008 2006 by Fabian Kung Wai Lee 44

Example 2.1 – Class-A Power Amplifier Design Cont…

• The results at PA = -5 dBm:

Eqn Zin = Vin/ISource.i

freq0.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

Zin<invalid>

36.417 + j17.783-1.000 + j0.000

-1.000 - j7.016E-17-1.000 + j0.000-1.000 + j0.000

Eqn PL = (mag(VL)*mag(VL))/(2*50)

freq0.0000 Hz868.0MHz1.736GHz2.604GHz3.472GHz4.340GHz

PL0.0000.013

3.031E-65.878E-91.475E-9

2.244E-100.5 1.0 1.5 2.00.0 2.5

-1.0

-0.5

0.0

0.5

1.0

-1.5

1.5

time, nsec

Vin

t, V

VLt

, V

Eqn VLt = ts(VL) Eqn Vint = ts(Vin)

Time-domain waveform at inputand load resistor

Page 23: Oscillator Design

23

September 2008 2006 by Fabian Kung Wai Lee 45

Example 2.1 – Class-A Power Amplifier Design Cont…

• Now we sweep the source PA to perform a gain compression test:

This defines the load andsource impedance at thefundamental and harnomics.Here we assume the circuitparasitics will short out thehigher harmonics

User can change theparameters in the Variable Equation"Stimulus_User_Setting"

Vin

VL

VSupply

HarmonicBalanceHB1

Step=1Stop=5Start=-20SweepVar="Ps_dBm"Order[1]=Max_HarmonicFreq[1]=RFfreq

HARMONIC BALANCEVARStimulus_User_Sett ings

Ps_dBm=-5Max_Rho=0.9Max_Harmonic=5RFfreq=868 MHzZo=50

EqnVar

VARLoad_Reflection_Coeffient

TLoad=TLArray[TLArrayIndex]TLArray=list(r(ZL_dc),TL,r(ZL_2),r(ZL_3),r(ZL_4),r(ZL_5),r(ZL_6),r(ZL_7))TLArrayIndex=int(min(abs(freq)/RFfreq + 1.5, length(TLArray)))

EqnVar

VARLoad_Reflection_Coefficient_Sweep

TL=TLcenter+TLmag*exp(j*(TLphase/180)*pi)TLcenter=0r(x)=(x-Zo)/(x+Zo)TLphase=0TLmag=0

EqnVar

VARLoad_Source_Impedance_at_Harmonics

Zs_7=1+j*0Zs_6=1+j*0Zs_5=1+j*0Zs_4=1+j*0Zs_3=1+j*0Zs_2=1+j*0Zs_1=ZoZs_dc=ZoZL_7=1+j*0ZL_6=1+j*0ZL_5=1+j*0ZL_4=1+j*0ZL_3=1+j*0ZL_2=1+j*0ZL_dc=1000000

EqnVar

VARSource_Impedance

Zs=ZsArray[ZsArrayIndex]ZsArray=list(Zs_dc,Zs_1,Zs_2,Zs_3,Zs_4,Zs_5,Zs_6,Zs_7)ZsArrayIndex=int(min(abs(freq)/RFfreq + 1.5, length(TLArray)))

EqnVar

CC3C=5.6 pF

CC4BC=0.68 pF

CC4AC=10.0 pF

LL2

R=L=4.7 nH

P_1TonePORT1

Freq=RFfreqP=polar(dbmtow(Ps_dBm),0)Z=Zs OhmNum=1

I_ProbeISource

CC1BC=0.47 pF

CC1AC=4.7 pF

LL1

R=L=8.2 nH

CC2C=8.2 pF

RRLR=50 Ohm

V_DCVccVdc=3.3 V

PA_coreX1

I_ProbeISupply

CCc1C=100.0 pF

CCc2C=100.0 pF

We sweep thevariable ‘Ps_dBm’

September 2008 2006 by Fabian Kung Wai Lee 46

Example 2.1 – Class-A Power Amplifier Design Cont…

• 1dB Gain Compression test result.

m1Ps_dBm=m1=10.738

-6.000

-15 -10 -5 0-20 5

0

5

10

-5

15

Ps_dBm

PL_

dBm

m1

Slope of 1Thus, P1dB ≅ 10.74 dBmmeeting our specs.

Page 24: Oscillator Design

24

September 2008 2006 by Fabian Kung Wai Lee 47

Example 2.1 – Class-A Power Amplifier Design Cont…

• Snapshot of the completed hardware.

September 2008 2006 by Fabian Kung Wai Lee 48

Example 2.1 – Class-A Power Amplifier Design Cont…

• Measurement at 868 MHz.

Freq. = 868 MHz+10.5 dBm

1st harmonic-11.0 dBm

Output of the amplifier when driven with a frequency synthesizer with Pin = -3.0 dBm into 50Ω load, fin = 868.0 MHz. Averaging = 10

Page 25: Oscillator Design

25

September 2008 2006 by Fabian Kung Wai Lee 49

Example 2.1 – Class-A Power Amplifier Design Cont…

• P1dB gain compression measurement.

+16 dB

+15 dB

1 dB Gain Compression point

September 2008 2006 by Fabian Kung Wai Lee 50

Typical Parameters for Medium Power Amplifiers

• Operating frequency range: 0.1-10GHz.

• Output power at 1dB gain compression: +15Bm (31.6mW) to +30dBm (1000mW).

• Power gain at 1dB gain compression: 12 - 20 dB.

• Furthermore VCE and IC will be specified for BJT and VDS and ID will be specified for FET. For MMIC, the supply voltage and current will be specified.

• Noise Figure: 3.0dB or greater.

• TOI input level: +10 to +15 dBm.

• TOI output level: +20 to +40 dBm.

• For MMIC, most of the time the source and load impedance is internally matched to 50Ω.

Page 26: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 51

3.0 Basic Mixer Design

September 2008 2006 by Fabian Kung Wai Lee 52

Mixers

• A mixer uses the nonlinearity of a diode, transistor or FET under large-signal operation to generate an output spectrum consisting of the sum and difference frequencies of two input signals.

• A mixer used for RF receiver usually consists of three ports, the RF, LO (Local Oscillator) and IF (Intermediate Frequency) ports.

• There are several types of mixers, the simplest being the Single-Ended Mixer. The single ended mixers are often used as components for more sophisticated mixers.

• The Balanced Mixer combines two or more identical single-ended mixer to give better input SWR or matching and higher isolation between the RF/LO ports.

RF

LO IF

Symbol andterminals ofa mixer

Page 27: Oscillator Design

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September 2008 2006 by Fabian Kung Wai Lee 53

Block Diagram of Single-Ended Mixer

Power supplyBiasing

InputMatchingNetwork

NonlinearElement

Low-pass FilterAndOutputMatchingNetwork

InputMatchingNetwork

PowerCombiner

RF

LO

IF

RF

LO IF

RFLOIF

LORFIF

fff

fff

−=−= or

PRF

PLO

PIF

RF

IF

PPAvailable

CG =Conversion Gain:

September 2008 2006 by Fabian Kung Wai Lee 54

Example of Single-Ended Diode Mixer

RFin1

Vcc

Rbias

Cc1Cc2

L2

L1

Cd

RL

Input matching network

Lumped version of Wilkinson Power Divider/Combiner (narrow band)

RFin2

Low-pass filter

RFC

RFC

Page 28: Oscillator Design

28

Simplified Analysis of the Diode Mixer

• Under DC condition the diode voltage and current are VD and ID.

• Imagine the RF chokes (RFC) present a high impedance to the AC voltage and current.

• The input AC voltage vd will modulate the diode junction voltage, which results in variation of the diode current id.

• The current flowing across the RFC is assumed constant, thus the change in current id is forced through the output of the mixer.

• Due to the nonlinear nature of the PN junction, id contains the sum and difference components.

December 2010 2006 by Fabian Kung Wai Lee 55

L2

L1

Cd

RFC

RFC

VCC

VD + vd ID High impedanceHigh

impedance idID + id

−≅+

+

1TnVdvDV

eIiI sdD

−= 1TnV

DV

eII sD

21 vvvd +=

( ) ( )[ ]L++≅

−=

2

211

T

d

T

dTnVDV

TnVdv

TnVDV

nVv

nVv

ssd eIeeIi

( ) ( )[ ]L++≅ ++ 2

21 2121

TT

TnVDV

nVvv

nVvv

sd eIi

Causes mixing effectAffectsconversiongain

DC:

DC with RF and LO:

( )tAv 111 cosω= ( )tAv 222 cosω=

Mixer Types (1)

• Following the definition by [4], mixer can be classified depending on the signaling type on the RF terminals.

• By signaling type we imply whether the RF input signal is single-ended or differential (double-ended).

• Sometimes two or more mixers can be combined to form a Balancedarchitecture.

May 2009 2006 by Fabian Kung Wai Lee 56

Single-Ended Mixer

RF

LO IF

Double-Ended Mixer

RF

LO IF

+ -

Differential RF input

Note:The LO input can besingle-ended ordifferential.

Page 29: Oscillator Design

29

Mixer Types (2)

• Balanced type mixers.

May 2009 2006 by Fabian Kung Wai Lee 57

RF

IF

Single-Ended Balanced Mixer(Single-balanced)

LO

PowerSplitter

PowerSplitter

PowerCombiner

Double-Ended Balanced Mixer(Double-balanced)

+

-RF

IF

LO

PowerSplitterwithbalun

PowerSplitter

PowerCombinerwith balun

May 2009 2006 by Fabian Kung Wai Lee 58

Conversion Gain and Leakage (1)

• If a diode is used for the nonlinear element, there is no gain, i.e. the conversion gain GC (dB) is negative. Sometimes this negative value is called conversion loss instead.

• If BJT or FET is used as the nonlinear element, there is usually a positive conversion gain GC (dB).

• A major issue with single-ended mixer is the leakage between the two RF inputs. This is due to the fact that the power combiner used is usually narrowband, and the frequency difference between RF and LO input is usually substantial.

RF

LO IF

Power Leakage

Power LeakageRF

LO IF

Power Leakage Power Leakage

Electrical energyinto LO terminalleaks out at RF andIF terminals.

Electrical energyinto RF terminalleaks out at LO andIF terminals.

Page 30: Oscillator Design

30

Conversion Gain and Leakage (2)

• The simplicity and performance of single-ended mixer make it very attractive in terms of cost, productivity and conversion loss. However this type of mixer usually exhibits higher leakage (e.g. lower isolation between ports), spurious products and low operating bandwidth.

• Leakage due to LO can be reduced by using differential RF input and differential IF output.

• Balanced mixers have better isolation between ports (lower leakage), lower spurious products. But this comes in terms of higher complexity, and usually larger conversion loss.

• A single-ended signal can be converted into differential signal and vice versa by using a Balun (balanced-unbalanced converter).

• Examples of balun are center-tapped transformer, and various type of directional couplers (see notes on RF Passive Circuits Design).

May 2009 2006 by Fabian Kung Wai Lee 59

September 2008 2006 by Fabian Kung Wai Lee 60

Example 3.1 – 430 MHz Single-Ended Discrete BJT Mixer Design

NOTE:By convention for a successful analysis of mixer:1. Set the RF input to PORT 1, IF output to PORT 2 and LO input to PORT 3 (by editing the NUM property).2. Set the signal with largest amplitude to Freq[1] to ensure convergence of the HB method.

Input matching network

Output matching network

VARVAR1

RF_pow=-20freq_RF=430 Mhzfreq_LO=410 Mhz

EqnVar

CCc2C=15.0 pF

CCdecC=1000.0 pF

OptionsOptions1

MaxWarnings=10GiveAllWarnings=yesI_RelTol=1e-6V_RelTol=1e-6TopologyCheck=yesTemp=23.85

OPTIONS

HarmonicBalanceHB1

Other=OutVar="RF_pow"NoiseOutputPort=2NoiseInputPort=1FreqForNoise=freq_RF-freq_LONLNoiseMode=yesOrder[2]=5Order[1]=7Freq[2]=freq_RFFreq[1]=freq_LOMaxOrder=7

HARMONIC BALANCE

DCDC1

DC

RRbR=47 kOhm

RR2R=1000 Ohm

P_1TonePrf

Freq=freq_RFP=polar(dbmtow(RF_pow),0)Z=50 OhmNum=1

TermTerm3

Z=50 OhmNum=2

P_1TonePLO

Freq=freq_LOP=polar(dbmtow(0),0)Z=50 OhmNum=3

LLm1

R=L=68.0 nH

I_ProbeISource

CCm3C=270.5 pF

LLm3

R=L=800.0 nH

CCm2C=97.0 pF

I_ProbeILoadC

Cc3C=330.0 pF

CCm1C=0.33 pF

CCc1C=330.0 pF

LLb

R=L=220.0 nH

CCbyp1C=1000.0 pF

V_DCSRC1Vdc=3.0 V

RReR=330 Ohm

pb_phl_BFR92A_19921214Q1

For more information, please refer to the document entitled:“Designing A Single-Ended UHF BJT Mixer Using the ADS Software” Sep 2001 by F.Kung.http://pesona.mmu.edu.my/~wlkung/ADS/ads.htm

Adding a series LC network (from E to Gnd)tuned to IF frequency will boostthe conversion gain, at the expense of larger LO leakage through RF input.

RF = 430 MHzLO = 410 MHzIF = 20 MHz

IF

LO

RF

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September 2008 2006 by Fabian Kung Wai Lee 61

Example 3.1 Cont...

RF source: frequency = 430.0MHz, Power = -20dBm into 50Ω load.LO source: frequency ≈ 410 MHz , Power = -5.48dBm into 50Ω load.Power supply for mixer: 3.0V.

Local Oscillator Input

RF InputIF Output

To 2.7-3.3V D.C. Source

1.57mm thick FR4 printed circuit board

BNC to PCB adapter

SMA to PCB adapter

Measurement at IF output, around 17MHz

≅60ns

Simplified Analysis of the BJT Mixer

• A similar analysis as in the diode mixer can be applied to the single-ended BJT mixer.

• Since there is current amplication (β), there is the possibility of conversion gain greater than unity.

• The variation in the BE voltage can be injected by the approach shown on the diagram or using a power combiner.

December 2010 2006 by Fabian Kung Wai Lee 62

−= 1TnV

BEV

eII EOC β

VBE+vRF-vLO vLO

vRF

High impedance

High impedanceICQ

ICQ+ic

ic

At DC:

DC with RF and LO:

−≅+

++

1TnVRFvLOvBEV

eIiI EOcC β

( ) ( )[ ]L++≅⇒++ 2

21

T

LORF

T

LORFTnVBEV

nVvv

nVvv

EOc eIi β

Transistor’s βand VBE

affects theconversiongain

Causes mixing effect

Let VBE be the DC bias, vRF and vLO are theAC RF and LO voltages:

( ) ( )( )

−+++≅+⇒ ++ 11

2

21

LT

LORF

T

LORFTnVBEV

nVvv

nVvv

EOcC eIiI β

Considering only the AC term (ic):

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September 2008 2006 by Fabian Kung Wai Lee 63

Example 3.2 – 868 MHz Single-Ended Discrete BJT Mixer Design

CCc2C=470.0 pF

CCB1C=470.0 pF

CCB2C=100.0 pF

CCD1C=100.0 pF

CCD0C=2.2 uF

RRD1R=100 Ohm

PortVCCNum=4

RRD2R=4.7 kOhm

DiodeDD2Model=LSR976

DiodeDD1Model=BZX284-C3V3

PortIF_outNum=2

PortLO_inNum=3

PortRF_inNum=1

CC1BC=1.5 pF

CC1AC=1.5 pF

LL1

R=L=33.0 nH

CC2C=22.0 pF

CCc1C=3.3 pF

CC3C=4.7 pF

CC4C=1.5 pF

LL2

R=L=10.0 nH

RRCR=470 Ohm

pb_phl_BFR92A_19921214Q1

CC5C=100.0 pF

LLC

R=L=100.0 nH

RRB1R=470 Ohm

LLB

R=L=100.0 nH

RRB2R=1.8 kOhm

RRB3R=100 Ohm

RF = 868 MHzLO = 818 MHzIF = 50 MHz

Power Supply

LO Input

RF Input

IF Output

Power combiner

September 2008 2006 by Fabian Kung Wai Lee 64

Example 3.2 Cont…

• Snapshot of the Mixer prototype.

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September 2008 2006 by Fabian Kung Wai Lee 65

Example 3.2 Cont…

• Measurement setup.

50.0 MHz, -22 dBm

A RF signal generator, IFR2023B supplies the RF signal to the mixer RF input, at 868.0 MHz and -20.0 dBmpower level (into 50Ω load). The frequency synthesizer built for this project drives the LO input, at 818.0 MHz and -2.4 dBm power level (into 50Ω load).

September 2008 2006 by Fabian Kung Wai Lee 66

Example 3.2 Cont…

• LO leakage at the RF terminal output.

818.0 MHz, -12 dBm

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September 2008 2006 by Fabian Kung Wai Lee 67

Block Diagram of Single-Balanced Mixer (1)

RF and LO power isdivided equally to the two identical single-ended mixer.Hence the term ‘balanced’

RF

Rbias

Cc2

L1

Vcc

Cd

RL

Cc1

L2

Input matching network

LO

Cc3

L3

Cc4

Input matching network

Low-pass filter

Low-pass filter

PowerCombi-ner

3dB Hybrid(90o or 180o)

The RF and LO inputs aresplit into 2 equal halves andimposed on the 2 diodes.This type of configuration isbetter known as Single-BalancedMixer.

September 2008 2006 by Fabian Kung Wai Lee 68

Block Diagram of Single-Balanced Mixer (2)

• 3dB hybrid directional coupler or junction (either 90o or 180o) are used to combine two identical single-ended mixers.

• 90o hybrid junction gives better wideband input SWR at the RF and LO inputs (this principle is also used in balanced amplifier).

• 180o hybrid junction gives better RF/LO isolation. This balanced mixer can also suppress even harmonics of LO input.

• Both types can also give cancellation of AM noise from the local oscillator.

• For details of mathematical analysis see chapter 10 of Pozar [8].

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More on Mixer Types

• Double-Balanced Mixer - suppresses even harmonics of both LO and RF inputs. Give good conversion gain. Also has good RF/LO isolation. Can be implemented using diode ring or using differential amplifier on integrated circuit.

• Image Rejection Mixer.

• In integrated circuit, a double-balanced mixer can be implemented using the ‘Gilbert Cell’, which is a modification of the two-quadrant analog multiplier. The two-quadrant analog multiplier is essentially an emitter (or source coupled) differential amplifier. See Gray & Meyer [7]. Most commercial integrated circuit mixer uses this method.

Example 3.3 - Double-Ended Balanced Mixer in Integrated Circuit

• This type of mixer is called the Gilbert Cell/Mixer.

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Vcc

+

-

v2

-

+

v1

Vout = R(Ic1 - Ic2)+

-

R RIc1 Ic2

IEE

Differential input:Hence the termdouble-ended.

PopularGeneral purposeGilbert cellmixer ICs:MC1496 – 100 MHzSA602AD – 200 MHzSA612AD – 500 MHzAD8342 – 500 MHz

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Example 3.4 - Discrete Double-Ended Balanced Mixer Using Diode Ring

Bottom Side

Another varactor-tuned

BPFImplemented on the PCBitself

Implemented on the PCBitself

PortTP5003Num=5

JUNCAPD5005Model=JUNCAPM1

JUNCAPD5004Model=JUNCAPM1

Diode_ModelDIODEM1

PortPIFNum=3

LL5008

R=L=470.0 nH

CC5052C=82.0 pF

LL5051

R=L=150.0 nH

RR5051R=51 Ohm

LL5004b

CC5055

LL5004a

PortPRFE2Num=1

CC5019-23C=77.0 pF

CC5024C=1.0 nF

RR5012R=100 kOhm

RR5060R=330 kOhm

PortFECTRLNum=2

Juncap_ModelJUNCAPM1MSUB

MSub1

T=1.38 milCond=5.8E+7Er=4.5

MSub

RR5052R=0 Ohm

DiodeDIODE2Model=DIODEM1

DiodeDIODE1Model=DIODEM1

DiodeDIODE3Model=DIODEM1

DiodeDIODE4Model=DIODEM1

XFERTAPT5052

XFERPT5051a

XFERPT505b1

CC5030

CC5032C=8.2 pF

CCL5005

LL5005b

LL5005a

CC5053C=6.8 pF

LL5053

R=L=15.0 nH C

C5054C=16.0 pF

LL5054

R=L=15.0 nH

PortRXINJNum=4

LL5009

R=L=1.0 nH

CC5031C=1.0 pF

MLINTL1

L=100.0 mi lW=25.0 milSubst="MSub1"

CC5017-18

CC5029

RF power flow

IF power flow

Diode ring

Balun

IF trap, tuned to 44.85MHz, shunts IF leakage to ground

September 2008 2006 by Fabian Kung Wai Lee 72

Typical Performance Parameters for Commercial Mixers

• Parameters for an integrated circuit mixer in the 1-3GHz range (for RF power = -20dBm, LO power = -5dBm, Zo=50Ohm, VCC = 5.0V).

• Power supply: single polarity, 4.0-8.0V.

• Typical LO power requirement: -5dBm.

• Conversion gain GC: 6.5 - 10dB.

• Single Sideband (SSB) noise figure: 17dB.

• LO leakage at IF port: -25dBm.

• LO leakage at RF port: -30dBm.

• VSWR: RF - 1.5, LO - 2.0, IF - 1.5.