The ABC’s of PA’s -...
Transcript of The ABC’s of PA’s -...
Berkeley
The ABC’s of PA’s
Prof. Ali M. Niknejad
U.C. BerkeleyCopyright c© 2014 by Ali M. Niknejad
Niknejad Advanced IC’s for Comm
Class A Review
Niknejad Advanced IC’s for Comm
Class A Amplifiers
Class A amplifiers have a collector current waveform with100% duty cycle. In other words, the bias current IQ > io ,where io is the current swing.
The advantage of Class A amplifiers is high linearity, cleansinusoidal waveforms (little harmonic filtering needed), andsimple design (not relying too much on transistornon-linearity).
The disadvantage of Class A is low efficiency and maximumpower consumption at zero output power!
Dynamic Class A (modulate bias current) is an attractivesolution for some applications. Envelope following Class Acombined with dynamic Class A is even better.
Niknejad Advanced IC’s for Comm
CE/CS Class A
vin
vo
VCC
RL
The CE amplifier has the advantage of higher power gain(there is voltage gain and current gain).
The collector effciency is given by
ηc =PL
Pdc=
12vo io
VCC IQ=
1
2v × i
The efficiency is maximized if we can set the voltage swingand current swing independently.
Niknejad Advanced IC’s for Comm
CE/CS Voltage Swing
VCC − VCE!sat
VCE!sat
VQ,low
VQ,high
VQ,mid
VCC
VCE,sat
VQ,mid
We see that to avoid clipping, we should bias the transistor atthe midpoint between VCC and VCE ,sat (or Vdsat).
Thus
vo ≤VCC
2
Niknejad Advanced IC’s for Comm
CE/CS Current Swing
IQ
0A
The current in the transistor cannot go negative. Therefore,the maximum current is set by the bias current
io ≤ IQ
The efficiency is therefore limited to 25%
η = v × i =1
2× 1
2
Niknejad Advanced IC’s for Comm
Optimum Load
It’s important to note that to achieve these optimumefficiencies, the value of the load resistance is constrained bythe current and voltage swing
Ropt =voio
=
(v
i
)(VCC
IQ
)Since the load resistance is usually fixed (e.g. antennaimpedance), a matching network is required to present theoptimum load to the amplifier.
Niknejad Advanced IC’s for Comm
Inductor Loaded CE/CS
vin
vo
VCC
RL
C∞RFC
If we AC couple a load RL to the amplifier, then the Q pointof the amplifier collector voltage is set at VCC through thechoke inductor.
The maximum swing is now nearly twice as large. Notice thatthe collector voltage can swing above the supply rail.
Niknejad Advanced IC’s for Comm
Swinging both ways...
vin
vo
VCC
RL
+VCC
−
+V
CC −VCC
−
+
Recall that the voltage polarity across the inductor is given bydI/dt, which can go negative. Thus the collector voltage isequal to the supply minus or plus the absolute voltage acrossthe inductor.
Niknejad Advanced IC’s for Comm
Improved Class A Efficiency
Since the swing is almost double, the efficiency nowapproaches 50%
vo ≤ VCC
η =1
2
iovoVCC IQ
≤ 1
2
In practice, due to losses in the components and back-off frommaximum swing to minimize distortion, the actual efciencycan be much lower.
Package parasitics (see later slides) also limit the voltageswing.
Niknejad Advanced IC’s for Comm
Complete Class A Output Stage
vin
vo
VCC
Lres
Cm
Lm R0Cpar
In practice the collector inductor can double as a resonantelement to tune out the collector parasitics.
The coupling capacitor Cc can be replaced by a matchingcapacitor Cm.
Niknejad Advanced IC’s for Comm
Class A Power Capacity
A good metric when comparing PA’s is to measure the outputpower versus the peak voltage and current stress imposed onthe device
These peak stresses are set by breakdown considerations. ForClass A operation, we can apply
PC =Pout
Vmax Imax
Vdrain,max = 2VDD
Idrain,max = IQ + IL = 2IQ
Pout =1
2VDD IQ
PC =1
2· 1
2· 1
2=
1
8= 0.125
Niknejad Advanced IC’s for Comm
Emitter Degeneration
Emitter inductance has adetrimental effect on PAefficiency since it reduces theswing. The voltage acrossthe emitter is given by
VE = jωLE io
vin
vo
VCC
RL
C∞RFC
+VLE
−
For a current swing of 1A at 1 GHz, a typical parasiticinductance of 1 nH will “eat” up 6.28V of swing! We need toreduce LE or to use a much higher VCC .
In practice both approaches are taken. We choose atechnology with the highest breakdown voltage and thepackage with the lowest LE .
Niknejad Advanced IC’s for Comm
Class B PA’s
Niknejad Advanced IC’s for Comm
Class B
+vin
−VCCvbias
The above circuit utilizes two transistors. Each device onlydelivers a half sinusoid pulse and the full sinusoid is recoveredby phase inversion through the transformer.
The base and collector bias voltages come from thetransformer center tap. The base (or gate) is biased at theedge of conduction (threshold).
Niknejad Advanced IC’s for Comm
Class B Waveforms
p(t)
ic(t) vc(t)
VCC
0V
Since the voltage at the load is ideally a perfect sinusoid, thevoltage on the collectors is likewise sinusoidal.
The power dissipated by each transistor is thus the product ofa sine and a half sine as shown above.
Niknejad Advanced IC’s for Comm
Class B Efficiency
The average current drawn by each transistor is given by
IQ =1
T
∫ T
0ic(t)dt =
IpT
∫ T/2
0sinωtdt =
Ip2π
∫ π
0sin θdθ =
Ipπ
Where Ip is the peak voltage drawn from the supply.
The peak current drawn from the supply is just the loadcurrent swing reflected to the collector, Ip = io × n.
η =1
2
(Ip
2IQ
)(vo
VCC
)Note that the total DC current draw is twice IQ since bothdevices draw current from the supply.
Niknejad Advanced IC’s for Comm
Class B Efficiency (cont)
Since the collector voltage swing can be as large as VCC
(similar to an inductively loaded Class A), the efficiency isbounded by
η ≤ 1
2
(Ip
2IQ
)=
1
4
(IpIQ
)η ≤ π
4≈ 78%
This is a big improvement over the peak efficiency of Class A.
Note that the average current naturally scales with outputpower, and so efficiency drops more gracefully as we back-offfrom peak power.
Niknejad Advanced IC’s for Comm
Efficiency versus Back-Off
η(V )
VCC
50%class B
class A
The efficiency drops linearly as we back-off from the peakoutput voltage
where vc is the collector voltage swing, which is just n timessmaller than the load voltage, vc = vo/n.
Niknejad Advanced IC’s for Comm
Tuned Class B
vin
vo
VCC
RL
C∞RFC
vbias
A tuned Class B amplifier works with a single devices bysending half sinusoid current pulses to the load. The device isbiased at the edge of conduction.
The load voltage is sinusoidal because a high Q RLC tankshunts harmonics to ground.
Niknejad Advanced IC’s for Comm
Class B Tank
In a single transistor version, the “minus” pulse is in factdelivered by the RLC tank. The Q factor of the tank needs tobe large enough to do this. This is analogous to pushingsomeone on a swing. You only need to push in one direction,and the reactive energy stored will swing the person back inthe reverse direction.
The average current drawn from the supply is the same asbefore, IQ = Ip/π. The harmonic current delivered to the loadis given by Fourier analysis of the half pulse
Iω1 =2
2πIp
∫ π
0sin θ sin θdθ =
1
πIp
∫ π
0
1− cos 2θ
2dθ
=1
π
π
2Ip =
Ip2
Niknejad Advanced IC’s for Comm
Class B Waveforms
ic(t) vc(t)
VCC
0V
We see that the transistor is cut-off when the collector voltageswings above VCC . Thus, the power dissipated during thisfirst half cycle is zero.
During the second cycle, the peak current occurs when thecollector voltage reaches zero.
Niknejad Advanced IC’s for Comm
Class B Efficiency (again)
The efficiency is therefore the same
η =1
2
Iω1
IQ
vcVCC
≤ 1
2
π
2=π
4
The DC power drawn from the supply is proportional to theoutput voltage
Pdc = IQVCC =VCC Ipπ
Ip =vc
Ropt=
nvoRopt
The power loss in the transistor is given by
pt(t) =1
2π
∫ π
0Ip sin θ(VCC − vc sin θ)dθ
Niknejad Advanced IC’s for Comm
Transistor Power Loss
Integrating the above expression
pt(t) =VCC Ip
2π(− cos θ
∣∣∣∣π0
− vcIp
2π
=1
2π
(2VCC Ip −
vc Ip2π
)=
Ipπ
VCC −vc Ip
4
= IQ · VCC −vc Iω1
2
= Pdc − PL
Niknejad Advanced IC’s for Comm
Class B Power Capacity
Recall the definition for PC
PC =Pout
Vmax Imax
Vmax = 2VCC
Imax = Iout
Note that the output power is related to the fundamentalcoefficient of a half sine wave, or 1/2 the peak
Pout =1
2VCC
Iout2
PC =12VCC
Iout2
2VCC Iout= 0.125
Same as Class A
Niknejad Advanced IC’s for Comm
Dynamic PA
vin
vo
Cm
Lm R0
DC-DC converterSupply
Envelope
Dynamic Bias
Envelope tracking supply and dynamic class-A
Efficiency always close to peak efficiency of amplifier (say30%) regardless of PAR
Need a very fast DC-DC converter
Niknejad Advanced IC’s for Comm
Class C PA’s
Niknejad Advanced IC’s for Comm
Conduction Angle
Often amplifiers are characterized by their conduction angle,or the amount of time the collector current flows during acycle.
Class A amplifiers have 360 conduction angle, since the DCcurrent is always flowing through the device.
Class B amplifiers, though, have 180 conduction angle, sincethey conduct half sinusoidal pulses.
In practice most Class B amplifiers are implemented as ClassAB amplifiers, as a trickle current is allowed to flow throughthe main device to avoid cutting off the device during theamplifier operation.
Niknejad Advanced IC’s for Comm
Reducing the Conduction Angle
ic(t) vc(t) ic(t) vc(t)
The most optimal waveform is shown above, where a currentpulse is delivered to the load during the collector voltageminimum (ideally zero)
As the pulse is made sharper and sharper, the efficiencyimproves. To deliver the same power, though, the pulse mustbe taller and taller as it’s made more narrow. In fact, in thelimit the current spike approaches a delta function.
Niknejad Advanced IC’s for Comm
Class C
vin
vo
VCC
RL
C∞RFC
Vbias < Vthresh
Class C amplifiers are a wide family of amplifiers withconduction angle less than 180. One way to achieve this is tobias a transistor below threshold and allow the input voltageto turn on the device for a small fraction of the cycle.
Niknejad Advanced IC’s for Comm
Class C Linearity
I
Q
000
001010
011
100
101110
111
I 2 + Q2 = A2
The Class C amplifier is very non-linear, and it is onlyappropriate for applications where the modulation is constantenvelope. For instance, FM uses a constant amplitude carrierand only modulates the frequency to convey information.Likewise, any digital modulation scheme with a constellationon a circle is constant envelope
Niknejad Advanced IC’s for Comm
Polar Modulation
RL
C∞
Vbias < Vthresh
B(t) cos (ωt + φ(t))A(t)
A0 cos (ωt + φ(t))
While the amplifier is a non-linear function of the inputamplitude, the Class C amplifier can be made to act fairlylinearly to the collector voltage.
By driving the amplifier into “saturation” in each cycle, e.g.with a large enough swing to rail the supplies, then the outputpower is related to the voltage supply. Collector modulationthen uses the power supply to introduce amplitudemodulation into the carrier.
Niknejad Advanced IC’s for Comm
Class C Approximate Analysis
IDD
IDQ2y
Assume current pulses are sine wave tips, conduction angle is2y
IDD cos y = IDQ y = cos−1(
IDQ
IDD
)iD(θ) =
−IDQ + IDD sin θ IDD cos θ ≥ IDQ
0 otherwise
Niknejad Advanced IC’s for Comm
Class C Average Current
To make the integral easy to calculate, change variables tothe range of y to 0.
IDC from supply:
IDC =1
2π
∫ 2π
0iD(θ)dθ =
1
π
∫ y
0(IDD cos θ′ − IDQ)dθ′
IDC =1
π(IDD sin y − IDQy)
IDC =IDD
π(sin y − y cos y)
Niknejad Advanced IC’s for Comm
Class C Analysis (cont)
Output voltage is: VOM = Fund−iD(θ)RLSince iD is an odd function, the Fourier series will only yieldsine terms
VOM =−2RL
2π
∫ 2π
0iD(θ) sin θdθ =
2RL
π
∫ y
0(IDD cos θ−IDQ) cos θdθ
VOM =2RL
π(
IDDy
2+
IDD sin 2y
4− IDQ sin y)
VOM =IDDRL
2π(2y − sin 2y)
Note: IDQ sin y = IDD cos y sin y = IDD2 sin 2y
DC power from prev page:PDC = IDCVCC = IDDVCC
π (sin y cos y)
Assuming that max swing ∼ VCC :
VOM ≈ VCC =IDDRL
2π(2y − sin 2y)
Niknejad Advanced IC’s for Comm
Class C Efficiency
PDC ≈2V 2
CC
RL
sin y − y cos y
2y − sin 2y
Power to load (assuming VCC swing): PL =V 2CC
2RL
Ideal Efficiency:
η =PL
PDC=
1
4
2y − sin 2y
sin y − y cos y
limy→0
η(y) = 100% (ideal class C)
η(π) = 50% (tuned-circuit Class A)
η(π/2) = 78.5% (single-ended Class B)
For small conduction angle current pulses approachdelta-function.Many practical issues make Class C difficult to design.
Niknejad Advanced IC’s for Comm
Power Capacity of Class C
0 50 100 150 200 250 300 3500.0
0.1
0.2
0.3
0.4
Class AClass B
Conduction Angle
Pow
er C
apab
ility
Vdrain,max = 2VCC
ID,max = IDD − IDQ
= IDD(1− cos y)
PC =Po
2VCC IDD(1− cos y)
=1
4π
2y − sin 2y
1− cos y
The power capacity of Class C is low at low conductionangles. Peak is Class AB.
Niknejad Advanced IC’s for Comm
Class D and F
Niknejad Advanced IC’s for Comm
Class F Circuit
3ω0
ω0 RL
The above circuit isolates the fundamental resonant load fromthe drain at the third harmonic, allowing the drain voltage tocontain enough third harmonic to create a more square likewaveform.
It can be shown that just adding a third harmonic boost theefficiency from 78% (Class B) to 88%.
Niknejad Advanced IC’s for Comm
Class F
ic(t) vc(t)
Since it’s difficult to create extremely narrow pulses at highfrequency, we can take a different approach and attempt tosquare up the drain voltage.
Niknejad Advanced IC’s for Comm
Quarter Wave Class F
ω0 RL
Z0
ℓ = λ0/4
RFC
In this circuit a quarter wave transformer converts the lowimpedance at the load (due to the capacitance) at harmonicsof the fundamental to a high impedance for all odd harmonics.Even harmonics are unaltered as they see a λ/2 line.
In theory then we can create a perfect square wave at thedrain of the transistor and thus achieve 100% efficiency.
Niknejad Advanced IC’s for Comm
Ideal Class D Switching Amplifier
S1
S2
RL
VDD
If give up linearity, then we can create some intrinsicallyefficient amplifiers using switches. An ideal switch does notdissipate any power since either the voltage or current is zero.
By varying the switching rate, we can impart phase/frequencymodulation onto the load.
A real switch has on-resistance and parasitic off capacitanceand conductance.
Niknejad Advanced IC’s for Comm
MOS Class D Inverter
RL
VDD
Switching amplifiers are realized with transistors operating asswitches. MOS transistors make particularly good switches.
The input voltage is large enough to quickly move theoperating point from cut-off to triode region.
Niknejad Advanced IC’s for Comm
Class D Waveforms
0V
id(t)VDDvd(t)
The MOS drain voltages switches from VSS to VDD at therate of the input signal.
A series LCR filter only allows the first harmonic of voltage toflow into the load. Since current only flows through a devicewhen it’s fully on (ideally VDS = 0), little power dissipationoccurs in the devices.
Niknejad Advanced IC’s for Comm
Class D Efficiency
We can see that the efficiency has to be 100% for an idealswitch. That’s because there is no where for the DC power toflow except to the load.
The collector voltage can be decomposed into a Fourier series
vd =VDD
2(1 + s(ωt))
s(θ) = sign(sin(θ)) =4
π
(sin θ +
1
3sin 3θ +
1
5sin 5θ + · · ·
)The load current is therefore
iL =4
π
VDD
2Rsin θ =
2VDD
πRLsin θ
Niknejad Advanced IC’s for Comm
Class D Efficiency (cont)
The load power is thus
PL =i2LRL
2=
2
π2V 2DD
RL≈ 0.2
V 2DD
RL
The drain current are half-sinusoid pulses. The averagecurrent drawn from the supply is the average PMOS current
IQ =Ipπ
=2
π2VDD
RL
PDC = IQ · VDD =2V 2
DD
πRL= PL
As we expected, the ideal efficiency is η = 100%
Niknejad Advanced IC’s for Comm
Class D Reality
As previously noted, a real Class D amplifier efficiency islowered due to the switch on-resistance. We can make ourswitches bigger to minimize the resistance, but this in turnincreases the parasitic capacitance
There are two forms of loss associated with the parasiticcapacitance, the capacitor charging losses CV 2f and theparasitic substrate losses.
The power required to drive the switches also increasesproportional to Cgs since we have to burn CV 2f power todrive the inverter. A resonant drive can lower the drive powerby the Q of the resonator.
In practice a careful balance dictates the maximum switchsize.
Niknejad Advanced IC’s for Comm
Differential Class D
VDC
RL
L1 C1
f0
+vin
−
+−vin
−
Differential circuit have a huge benefit in ICs. First they havecommon mode rejection and also inject (ideally) less commonmode into the supplies. Makes system integration easier (e.g.VCO pulling). Also differential allows higher swings on loadfor a fixed supply, and less impact from bond-wire inductors.
Downside: Need a balun.
Niknejad Advanced IC’s for Comm
Differential Class D Analysis
Assume a high Q tank so that the output current is sinusoidal(phase φ will be computed)
iout = Io sin(θ + φ)
The voltage at the secondary of the transformer is given by
vo(θ) = nVDC s(t)− n2IoRon sin(θ + φ)
The fundamental component of the secondary load voltage isgiven by
vL(θ) = RLiout = nVDC4
πsin(θ)− n2IoRon sin(θ + φ)
Niknejad Advanced IC’s for Comm
Class D Analysis (cont)
From the above relation, it’s clear that the voltage andcurrent are in phase (φ = 0)
Io =4nVDC
πRL
1
1 + n2 RonRL
Each transistor conducts a half sinusoid pulse (similar todifferential Class B), so it’s DC value is
id1,DC = id2,DC =nIoπ
The DC power consumed is therefore
PDC = VDC (id1,DC + id2,DC ) =8n2VDC
π2RL
1
1 + n2 RonRL
Niknejad Advanced IC’s for Comm
Class D Efficiency
From the AC and DC power, we are now in a position tocalculate the efficiency
Pout =1
2I 20 RL =
8n2V 2DC
πRL
1
1 + n2 RonRL
η =Pout
PDC=
1
1 + n2 RonRL
Note that the switch on resistance is a key factor. We cannotarbitrarily increase it due to CVf 2 losses.
Niknejad Advanced IC’s for Comm
Estimating Switching Losses
We can estimate the switching losses by noting that thedevice “on”-resistance is related to the device gds,lin = gm,sat
Ron =1
gds≈ 1
gm,sat
ωT =gm
Cgs + Cgd=
1
Ron(Cgs + Cgd)
The total input power involves switching approximately2Cgs + 2γCgs , where γ is a technology parameter relating thedrain-bulk capacitance to the gate-source cap. Take γ ∼ 1 foran upper bound
Ploss = CtotV2DC f = 4CgsV 2
DC f = 4V 2DC f
1
ωTRon
Niknejad Advanced IC’s for Comm
Class D Power Handling Capability
The power handing capability of Class D is given by
vdrain,max = 2VDD
idrain,max = nIo
PC =Pout
2 · vdrain,max · idrain,max=
η
2π≤ 0.159
This compares favorably with Class A amplifiers.
Niknejad Advanced IC’s for Comm
Class D−1
VDC
IDC
RL
L1
C1
f0
is1 is2i1
vs1 vs2
IDC is1
vs1
IDC
The “Dual” Class D amplifier (interchange voltage/current ⇒square wave current, sinusoidal voltage, parallel LCR filter)
Chokes act like current sources. ZVS by “design” but only ifthere is no device capacitance to begin with.
vs1 =
0 0 < θ < π
− 4π IDCRL sin(θ) π < θ < 2π
Niknejad Advanced IC’s for Comm
Class E
Niknejad Advanced IC’s for Comm
Class E Amplifier
Switching PA like Class D but can absorb transistor parasiticcapacitance into load network. This allows the switch tobecome very large (low on-resistance).
The load network is design to ensure zero switching condition.
Figures: “Class-E RF Power Amplifiers,” by Nathan O. Sokal,Design Automation, Inc
Niknejad Advanced IC’s for Comm
Switching RF Power Amplifier
Switching amplifier = LC network and a switch
Low Q
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Switching RF Power Amplifier
Switching amplifier = LC network and switch
High Q
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Switching RF Power Amplifier
Switching amplifier = LC network and switch
perfect Q
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Switching RF Power Amplifier
Switching amplifier = LC network and switch
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Switching RF Power Amplifier
Output power of Class E is low
Pout,E < 0.045V 2max
RLOAD
Compare to Class A
Pout,A < 0.125V 2max
RLOAD
0.35um technology, Vmax = 8V ⇒ Pout < 60mW at 50Ω
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Class E Waveforms
128
DD
o
V
L
πω
Figure 6-3 Circuit configuration and characteristic waveforms of a Class-E PA
CMOS Power Amplifiers for
Wireless Communication,
King-Chun Tsai, Ph.D.
Dissertation, UC Berkeley,
2007.
Niknejad Advanced IC’s for Comm
Class E Issues
Problems with Class E include low power gain and largevoltage swings. The drain waveform can swing to more than3.5 times the supply voltage. This means the transistors haveto be able to handle much larger voltages.
Efficiency for this class of PA is extremely good. Powercapacity PC < 0.107, much better than Class C lowconduction angle operation.
Niknejad Advanced IC’s for Comm
First GSM CMOS Class E
149
in each stage and significantly relaxes the input driving requirement. Inserting cross-
coupled pairs effectively turn each gain stage into an injection locking oscillator and we
will discuss the injection locking mechanism in greater details later in this chapter.
Figure 7-1 Schematic of the 1-W 1.9GHZ CMOS Differential Class-E power amplifier
Use standard CMOS to achieve output power of 1WMeasured efficiency > 50%Use cross-coupled devices to boost driver capability (requiresinjection locking)
CMOS Power Amplifiers for Wireless Communication, King-Chun
Tsai, Ph.D. Dissertation, UC Berkeley, 2007.
Niknejad Advanced IC’s for Comm
Output Matching
Use chip-on-board testing (avoid lead inductance)
Use a microstrip balun to convert from differential tosingle-ended to drive antenna
Source: “A 1.9-GHz, 1-W CMOS Class-E Power Amplifier forWireless Communications,” King-Chun Tsai and Paul R. Gray
Niknejad Advanced IC’s for Comm
RF CMOS Class-E PA
Implemented in a 0.18 um CMOS technology
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Chip micrograph
Source: Patrick Reynaert and Michiel Steyaert
Niknejad Advanced IC’s for Comm
Other Classes
Niknejad Advanced IC’s for Comm
Class S
If the switching rate is much higher than the fundamental,then amplitude modulation can be converted to pulse-widthmodulation.
A low-pass filter at the output faithfully recreates theenvelope of the signal.
Niknejad Advanced IC’s for Comm
Class S Amplifier
RL
VDD
Amplitudeto PWM
Class S amplifiers are commonly used at low frequencies(audio) since the transistors can be switched at a much higherfrequency than the fundamental.
This allows efficiencies approaching 100% with good linearity.
Niknejad Advanced IC’s for Comm
Pulse Density Modulation
RF Pulse Train
Pulse-density modulation process
Mixer PA Filter
Inherent linearity
Improved efficiency in power backoff, but ...
Niknejad Advanced IC’s for Comm
Pulse Density Modulation Process
AM process ⇒ Extra harmonics
Tradeoff between oversampling ratio and Q
Out of band spectrumEfficiency
Noise shaping: digital ∆− Σ
Conclusions
No major efficiency advantage with Q< 5-10Linearity may be the compelling factor(almost) pure digital implementation!Need to run PDM process *as fast as possible*
Niknejad Advanced IC’s for Comm