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Amplifier2 (RF System Amplifier)

Symbol

Available in ADS and RFDE

Parameters

Name

Description

Units

Default

S21

Forward transmission coefficient, use x + j × y, polar(x,y), dbpolar(x,y) for complex value

None

dbpolar(0,0)

S11

Forward reflection coefficient, use x + j × y, polar(x,y), dbpolar(x,y), vswrpolar(x,y) for complex value

None

polar(0,0)

S22

Reverse Reflection Coefficient, use x + j × y, polar(x,y), dbpolar(x,y), vswrpolar(x,y) for complex value

None

polar(0,180)

S12

Reverse Transmission Coefficient, use x + j × y, polar(x,y), dbpolar(x,y) for complex value

None

0

NF

Noise figure [NF mode used for NFmin=0]

dB

None

NFmin

Minimum noise figure at Sopt [(NFmin,Sopt,Rn) mode used for NFmin>0]

dB

None

Sopt

Optimum source reflection for minimum noise figure [(NFmin,Sopt,Rn) mode used for NFmin>0]

None

None

Rn

Equivalent noise resistance [(NFmin,Sopt,Rn) mode used for NFmin>0]

None

Z1

Reference impedance for port 1 (must be a real number)

None

Z2

Reference impedance for port 2 (must be a real number)

None

GainCompType

Gain compression type:

None

LIST

GainCompFreq

Frequency at which Gain Compression is specified

None

ReferToInput

Specify each of the gain compression options outlined in Polynomial Order for Various Magnitude Modes with respect to the input or output power of the device:

None

OUTPUT

SOI

Second order intercept

dBm

None

TOI

Third order intercept

dBm

None

Psat

Power saturation point (always referred to output, regardless of the value of the ReferToInput parameter)

dBm

None

GainCompSat

Gain compression at Psat

dB

5.0

GainCompPower

Power Level at gain compression specified by GainComp

dBm

None

GainComp

Gain Compression at GainCompPower

dB

1.0

AM2PM

Amplitude modulation to phase modulation

deg/dB

None

PAM2PM

Power level at AM2PM

dBm

None

GainCompFile

Filename for gain compression data in S2D file format

None

None

ClipDataFile

Clip data beyond maximum input power: YES=enable, NO=disable

None

yes

ImpNoncausalLength

Non-causal function impulse response order

Integer

None

ImpMode

Convolution mode

Integer

None

ImpMaxFreq

Maximum frequency to which device is evaluated

None

ImpDeltaFreq

Sample spacing in frequency

None

ImpMaxOrder

Maximum allowed impulse response order

Integer

None

ImpWindow

Smoothing window

Integer

None

ImpRelTol

Relative impulse response truncation factor

None

None

ImpAbsTol

Absolute impulse response truncation factor

None

None

Frequently Asked Questions

Q1 : What are the major differences between Amplifier and Amplifier2?
A1 : Refer to note 1.

Q2 : What are the supported parameter combinations?
A2 : Refer to Range of Usage.

Q3 : What is the range of usage for each parameter combination?
A3 : Refer to Range of Usage.

Q4 : What model is being used?
A4 : A polynomial model. Refer to Modeling Basics.

Q5 : What polynomial order is being used?
A5 : It depends on the parameters set on the component. Refer to Modeling Basics.

Q6 : Can these polynomials blow up?
A6 : No, these polynomials are limited. Refer to Modeling Basics for details.

Q7 : The parameters specified for Amplifier2 match those for my transistor level amplifier. Why don't the harmonics generated by Amplifier2 match those for my transistor level amplifier?
A7 : Amplifier2 only matches the specified parameters. Refer to Modeling Basics for details.

Q8 : I have a small-signal and a large-signal tone. Why does the small-signal tone have a smaller gain than the large-signal tone?
A8 : It is a consequence of the polynomial model adopted by Amplifier2. Refer to Modeling Basics for details.

Q9 : In a swept-power harmonic halance simulation, my higher-order harmonics are zero up to a certain order but then they suddenly experience a very sharp increase. Isn't this wrong?
A9 : No, it's called generating a square wave via hard limiting. Refer to Modeling Basics for details.

Q10 : How do I validate AM to PM conversion?
A10 : Refer to AM to PM Conversion.

Q11 : Why does AM to PM conversion only match my transistor level amplifier around the power level PAM2PM at which I specified AM2PM?
A11 : With information at only one power level, Amplifier2 has to rely on assumptions and generic curve shapes to model AM to PM at all power levels. For better modeling, use an S2D file and specify the exact magnitude and phase variation of your amplifier. Refer to AM to PM Conversion for details.

Q12 : With AM to PM conversion enabled, my output phase is supposed to be constant at high power levels. Why does my AM to PM start changing at high power levels?
A12 : This is probably due to harmonic balance aliasing errors and can be mitigated by oversampling. Refer to AM to PM Conversion for details.

Q13 : With AM to PM conversion enabled, why don't the predicted second- and third-order intercept points match SOI and TOI as set on Amplifier2?
A13 : It is a consequence of fitting the magnitude and phase separately. Refer to Refer to AM to PM Conversion for details.

Q14 : Why do Amplifier2's noise results differ from those for Amplifier?
A14 : Amplifier2 models noise differently from Amplifier. Refer to Noise for details.

Q15 : What noise model is used by Amplifier2?
A15 : Refer to Noise.

Q16 : What is "NF-only mode" and "(NFmin,Sopt,Rn) mode" for Amplifier2?
A16 : It is two different ways of specifying noise. Refer to Noise for details.

Q17 : How is NFssb/NFdsb calculated, both at low powers and in compression?
A17 : Refer to Noise.

Q18 : Can you provide more details about the noise voltages and noise figures produced by Amplifier2 for the different modes of operation?
A18 : Refer to Noise .

Q19 : With complex S21, why does Amplifier2 differ from Amplifier?
A19 : Amplifier2 handles complex S21 values differently from Amplifier, leading to more physical waveforms. Refer to note 5 for details.

Q20 : Why doesn't Amplifier2 work for complex reference impedances?
A20 : Amplifier2 does not support complex reference impedances, per note 7.

Q21 : Why is Amplifier2 sometimes slower than Amplifier?
A21 : This is a consequence of the implementational differences between Amplifier and Amplifier2. Refer to note 10 for details.

Q22 : Why don't the predicted second- and third-order intercept points match SOI and TOI as set on Amplifier2?
A22 : You are probably not setting up your validation correctly. Make sure to do a two-tone simulation, not a one-tone simulation. Refer to note 11 for details.

Q23 : Why does my ACPR level get better as I get deeper into compression?
A23 : This is a consequence of the polynomial model adopted by Amplifier2. Refer to note 12 for details.

Q24 : Why does Amplifier2 ignore the ACDATA block of my S2D file?
A24 : It uses the S-parameters on the component instead. Refer to note 13 for details.

Q25 : When the power range in an S2D file differs from that of a simulation, which power range is used for polynomial fitting?
A25 : The power range in the S2D file. Refer to note 15 for details.

Q26 : Why do I get ringing at high powers when using an S2D file?
A26 : This is a consequence of the polynomial model adopted by Amplifier2. Refer to note 16 for details.

Q27 : How do I get rid of this ringing?
A27 : Eliminate data for high input powers, rely on extrapolation via ClipDataFile=yes, or break the S2D file into two. Worst case, use AmpSingleCarrier. Refer to note 16 for details.

Q28 : Why do I see different results when I use the Analog/RF Amplifier2 component and the Ptolemy GainRF component with the same parameters?
A28 : While based on the same OmniSys legacy, the implementations differ and thus the components can give different results. Refer to note 18 for details.

Range of Usage

|Sij| > 0 (i=1,2; j=1,2)
NF ≥ 0 dB
NFmin ≥ 0 dB
0 < |Sopt| < 1
Rn > 0
GainCompFreq > 0
0 dB < GainComp < 3 dB

When specifying gain compression using model parameters, only certain combinations of parameters will produce stable polynomial curve fitting. If unrealistic parameter values are used, the polynomial will become unstable, resulting in oscillations. The recommended parameter combinations are listed here:

  • Third-order intercept parameter:
    Parameters: TOI
    Range of validity: N/A
  • Gain compression parameters:
    Parameters: GainCompPower, GainComp
    Range of validity: N/A
  • Power saturation parameters:
    Parameters: Psat, GainCompSat
    Range of validity: N/A
  • Third-order intercept and 1dB gain compression parameters:
    Parameters: TOI, GainCompPower with GainComp=1dB
    Range of validity: TOI > GainCompPower + 10.8
  • Third-order intercept and power saturation parameters:
    Parameters: TOI, Psat, GainCompSat
    Range of validity: TOI > Psat + 8.6
  • 1dB gain compression and power saturation parameters:
    Parameters: GainCompPower with GainComp=1dB, Psat, GainCompSat
    Range of validity: Psat > GainCompPower + 3
  • Third-order intercept, 1dB gain compression and power saturation parameters:
    Parameters: TOI, GainCompPower with GainComp=1dB, Psat, GainCompSat
    Range of validity: Psat > GainCompPower +3, TOI > GainCompPower + 10.8
  • Second-order intercept and third-order intercept parameters:
    Parameters: SOI, TOI
    Range of validity: N/A

Modeling Basics

Amplifier2 is based on a polynomial model of the magnitude of the output voltage as a function of the input voltage. If SOI is not specified, the magnitude response is modeled using a polynomial of odd orders
y = a1 × x + a3 × x3 + a5 × x5 + ...
The order of the polynomial depends on the data entered by the user. If SOI is specified, the magnitude response has an even order term
y = a1 × x + a2 × x2 + a3 × x3
The order of the polynomial is hardwired at 3. The polynomial orders for the various magnitude modes are summarized in Polynomial Order for Various Magnitude Modes.

Magnitude Mode

Polynomial Order

TOI

3

SOI, TOI

3 (with second-order term)

GainCompPower, GainComp

3

Psat, GainCompSat

5

TOI, GainComp=1dB, GainCompPower

5

TOI, Psat, GainCompSat

7

GainComp=1dB, GainCompPower, Psat, GainCompSat

7

TOI, GainComp=1dB, GainCompPower, Psat, GainCompSat

9

For GainCompType=LIST, the phase response is described in the section AM to PM Conversion. For GainCompType=FILE and a GCOMP1-GCOMP6 block in the S2D file, the phase response is zero. For GainCompType=FILE and a GCOMP7 block in the S2D file, the phase response is modeled using an odd order polynomial, just like the magnitude response.

To prevent these polynomial expressions from blowing up and resulting in a non-physical model, the polynomial model is only used up to the largest x fulfilling dy/dx=0, denoted by x0. Above this value, the amplifier is hard-limited at y(x0).

The polynomial coefficients for Amplifier2 are based on the parameters set for Amplifier2 regardless of the context in which Amplifier2 is used and the actual number of tones at the input of Amplifier2. These polynomial coefficients are then applied when Amplifier2 is analyzed in the environment where it lives. For example, given GainComp and GainCompPower, the polynomial coefficients are determined by exciting Amplifier2 with a one-tone signal and requiring the compressed output power to be GainComp below the linear response at GainCompPower. This can be confirmed by doing a one-tone analysis of Amplifier2. These polynomial coefficients are then used in any analysis using Amplifier2, whether it be a one-tone or a multi-tone analysis.

Amplifier2 matches the parameters that have been set on the component but is not guaranteed to match any other characteristics of a transistor level amplifier. Assume three parameters have been specified for Amplifier2: the linear gain S21, the 1 dB compression point GainCompPower (GainComp is set to 1 dB), and the third-order intercept TOI. This means that the behavior of Amplifier2 must match these parameters and nothing else. This is achieved by modeling y as a function of x via y = a1 × x + a3 × x3 + a5 × x5. The three known quantities allow the determination of the three unknown polynomial coefficients. If we look at this equation, we see that there is a fifth-order term. Therefore, Amplifier2 will produce fifth-order harmonics. However, this fifth-order order term is not supposed to match that from the transistor level amplifier from which the three parameters S21, GainCompPower and TOI were extracted. No information about the fifth-order intercept of that amplifier has been specified so we cannot match it. The fifth-order term for Amplifier2 is necessary to properly model S21, GainCompPower and TOI and these parameters are properly modeled. In general, a transistor level amplifier will produce finite higher order harmonics which Amplifier2 does not produce.

For GainCompType=FILE and a GCOMP7 block in the S2D file, the magnitude and phase data in the GCOMP7 block of the S2D file is fitted to two separate polynomials. With n power points in the GCOMP7 block, the polynomial order will be min(2 × n -1,9). In most practical cases, the GCOMP7 block will have data at five or more power points and consequently ninth-order polynomials with odd-only terms will be used.
Consider now an amplifier with the response

This is the model used when S21, SOI and TOI are specified. If a2 and a3 are non-zero, they will be negative. When a2=0, this is the model used when S21 and TOI are specified. When a2=a3=0, this represents a linear amplifier. The behavior of this amplifier can be analyzed analytically when the excitation is simple enough. Doing so gives a good understanding of the behavior of more complicated amplifiers with different excitations.
Assuming the excitation

we get the response

and can define the gain of the fundamental A1 × cos(ω1 × t) as

Assuming the excitation

we get the response

and can define the gain of the fundamentals A1 × cos(ω1 × t ) and A2 × cos(ω2 × t ) as

and

respectively.

Examining G1 and G2 closer, we see that G1>G2 for A1>A2 and a3<0. This means that if we excite a polynomial amplifier with a large- and a small-signal tone, the large-signal tone will experience a larger gain than the small-signal tone. For more details, please refer to "Polynomial Model of Blocker Effects on LNA/Mixer Devices" by W. Domino et. al. in the June 2001 issue of Applied Microwave and Wireless.

This behavior is counter-intuitive for some people. If we excite an amplifier with a small-signal tone, it will provide its maximum/linear gain. If we excite the same amplifier with a large-signal tone, it will provide a smaller/compressed gain. If we excite an amplifier with both a large- and a small-signal tone, one could then expect that the small-signal tone would be subject to a larger gain than the large-signal tone. The above shows that this is not how Amplifier2 behaves.

This behavior, however, is intuitive for some people. If we consider an ideal hard limiting amplifier with an input voltage of Vin and an output voltage of Vmax, it has a large-signal gain of Vmax/Vin but a small-signal gain of zero, suggesting a larger large-signal gain than small-signal gain. This is in line with how Amplifier2 behaves.

Above, we presented the polynomial model used for modeling the output voltage as a function of the input voltage. This polynomial model, however, does not fully describe the response of the amplifier. It is important to remember that the amplifier has a power level at which it saturates and above which the output is clipped. We also presented the result of pushing A1 × cos(ω1 × t) and A1 × cos(ω1 × t)+A2 × cos(ω2 × t) signals through a y = a1 × x + a2 × x2 + a3 × x3 nonlinearity. The result is an output voltage consisting of a finite number of Cn × cos( n × ω n × t ) terms. More generally, it can easily be shown that pushing a sum of Ai × cos( ω i × t ) terms through a polynomial nonlinearity will result in a finite number of Cn × cos( n × ω n × t ) terms. It might then be expected that a harmonic balance analysis of such an amplifier can only produce finite harmonics up to a certain order but will always produce zero harmonics beyond a certain order. This is the case when the amplifier is not hard limiting but is not the case when the amplifier starts hard limiting.

When we analyze an amplifier via a harmonic balance simulation of a certain order, the harmonics we will see on the input and output of the amplifier will be those which lead to the most correct input and output waveforms that can be achieved with the given order.

Assume the input waveform is a sine wave. This can be represented exactly using only the fundamental. Therefore, we will see a finite fundamental tone and zero harmonics on the input.

The output waveform depends on the input power level.

At low input powers, the output waveform is simply a sine wave, namely the input sine wave scaled by the linear amplifier gain. This can be represented exactly using only the fundamental. Therefore, we will see a finite fundamental tone and zero harmonics.

At higher input powers where the amplifier enters compression, the output waveform is the input sine wave pushed through the amplifier polynomial. Because a sine wave pushed through a polynomial gives rise to sine terms and no others, the output waveform will have finite harmonics up to a certain order and zero harmonics above that order.

At high enough input powers that the amplifier starts hard limiting, the output waveform is a clipped sine wave. For increasingly high input powers, this clipped sine wave approaches a square wave. Representation of such a clipped wave requires finite third, fifth, seventh, etc. harmonics so when the amplifier starts clipping all harmonics will be finite. This means that we will see a very sharp increase in the level of all such harmonics as soon as the amplifier starts clipping. If we increase the input power enough, we get approximately a square wave output. When this happens, the levels of the various harmonics reach saturation. The relative values of these saturated power levels can be predicted from the Fourier representation of a square wave.

AM to PM Conversion

The Amplifier component supports AM to PM conversion for a very limited number of magnitude modes; Amplifier2 supports AM to PM conversion for all magnitude modes when GainCompType=LIST. Magnitude and phase is fitted separately so AM to PM conversion can be added for each magnitude mode. This adds a phase response but does not alter the magnitude response.

AM to PM conversion is defined as the amount of phase change in degrees per magnitude/power change in dB. It is specified via the two parameters AM2PM and PAM2PM. AM2PM [degrees/dB] is the amount of AM to PM conversion while PAM2PM [dBm] is the power level at which the amplifier has this amount of AM to PM conversion. A physically sensible phase response is then constructed which has a phase of phase(S21) at low powers, an amount of AM to PM conversion given by AM2PM at PAM2PM, constant phase at high powers and for which the maximum amount of AM to PM at any power level is also given by AM2PM. Stated differently, the derivative of the phase response with respect to power in dB takes its maximum value AM2PM at PAM2PM.

This phase response is far from unique and certainly will not be correct for all amplifiers. Based only on the amount of AM to PM at one power level, there is simply no way to construct a phase response that matches any circuit level amplifier at all power levels. This AM to PM capability is only meant as a crude way of incorporating a phase response for amplifiers about which very little information is known - at the initial system level design iterations, For example, where no transistor level amplifier has been designed. Once more information about the amplifier's phase response is known and a more accurate phase modeling is desired, use Amplifier2 with GainCompType=FILE and specify the (compression and) phase response as a function of power in the GCOMP7 block of an S2D file. This is much more accurate than what this AM to PM capability can provide.

To document the exact phase response in a little more detail, we start out with AM2PM [degrees/dB] and PAM2PM [dBm]. We first define:
k=AM2PM
P=10(PAM2PM-30)/10
For a sine wave
A0 × cos(ω × t)
the average power is

Therefore, we have

The phase response is initially modeled in the A-domain. We choose
y(A)=c0+c1 × A+c2 × A2+c3 × A3
We now get
y(0)=0 -> c0=0
dy/dA(0)=0 -> c1=0
dy/dA(A0)= k -> 2 × A0 × c2+3 × A02 × c3=0
d2 y / dA2 (A0)=0 -> c2+3 × A0 × c3=0
c2=k/A0
c3=- k /(3 × A02 )
Then, we have
y(A)= k / A0 × A2 - k /(3 × A02 ) × A3
This function has the following properties
y(0)=0
dy / dA(0)=0
y (A0)=2/3 × k × A0
dy / dA(A0)=k
d2 y / dA2 (A0)=0 (A0 is an extremum, max AM to PM occurs here)
y (2 × A0)=4/3 × k × A0=2 × y (A0)
dy / dA (2 × A0)=0

This curve will be distorted when it is made a function of power in dBm instead of magnitude A. The difference between two log values can be quite significant at small values but will be much smaller at large values. This means that the log function will distort the curve - it will be stretched out at low powers and will be compressed at high powers. This will change the point where the maximum slope occurs so the curve is shifted/scaled such that the maximum slope AM2PM occurs at PAM2PM. Also, we account for the fact that the derivative with respect to A must be in dB and not linear numbers.

The above phase response applies to the fundamental tone. This phase shift is applied before the application of the nonlinear polynomial which means that the change of the phase response of the nth order harmonic from its low power value will equal that for the fundamental tone scaled by the harmonic index n.

The easiest way to validate that the amount of AM to PM conversion takes its maximum value AM2PM at PAM2PM is to use the diff function in ADS. If the Amplifier2 output voltage is denoted by Vout and determined via a swept input power harmonic balance simulation, simply plot diff(phase(Vout[::,1])). The peak of this curve should occur at PAM2PM and should take the value AM2PM.

All harmonic balance simulations can be subject to aliasing errors. This can significantly change the phase response of an amplifier. To mitigate the effects of harmonic balance aliasing errors, increase the Fundamental Oversample (FundOversample) parameter on the HarmonicBalance controller from the default 1 to, say, 16.

The magnitude and phase response for Amplifier2 are fitted separately. Given, say, SOI and TOI, a set of magnitude polynomial coefficients are determined such that Amplifier2 has a second-order intercept point of SOI and a third-order intercept point of TOI. Given AM2PM and PAM2PM, a set of phase polynomial coefficients are determined such that Amplifier2 has AM to PM conversion given by AM2PM at PAM2PM. When using an Amplifier2 with both a magnitude and a phase response in a multi-tone harmonic balance simulation, there is no guarantee that the above magnitude and phase separation will hold. Generally, a phase response will generate intermodulation distortion with a multi-tone input. This is part of why AM to PM conversion is of interest. This means that the third-order intercept point may no longer be the TOI set on the component. Amplifier2 makes no attempt at matching the composite magnitude/phase third-order intercept point to the TOI set on the component but simply uses the polynomial coefficients derived for the isolated magnitude mode.

Noise

Given the minimum noise figure NFmin (real), the optimal reflection coefficient Sopt (complex), the noise resistance Rn (real), the noise reference impedance Rref (real), and the source admittance Ys (complex), the noise figure NF of an amplifier is determined by:

Note that this is independent of the amplifier S-parameters.

The noise behavior of Amplifier2 is characterized by the four noise parameters NF, NFmin, Sopt and Rn and the reference impedance Z1 for port 1. Amplifier2 is implemented as a Noisy2Port cascaded with an SDD. The above-mentioned five parameters control the parameters for the Noisy2Port, the Noisy2Port generates a noise voltage on its output and this noise voltage is passed through the SDD in the same manner as the signal.

NF-only mode is used for NFmin=0. This is a special case where only one noise parameter must be specified. In this case, the Noisy2Port has the parameters NFmin=NF, Sopt=0, and Rn=Z1/4 × (10NF/10-1). The reference impedance for the noise calculation (not available on the Noisy2Port user interface) is Z1. The NFmin=0, Sopt and Rn parameters are ignored.

(NFmin, Sopt, Rn) mode is used for NFmin>0. This is a more general case than NF-only mode. In this case, the Noisy2Port has the parameters NFmin=NFmin, Sopt=Sopt, and Rn=Rn. The reference impedance for the noise calculation (not available on the Noisy2Port user interface) is Z1. The NF parameter is ignored.

Given an output noise voltage vn, the single sideband noise figure NFssb and the double sideband noise figure NFdsb are given by:
NFssb=10*log ((vn2 / R + k × T0 × (G1 + G2 +...)) / (k × T0 × G1))
NFdsb=10*log( (vn2 / R + k × T0 × (G1+G2 + ...)) / (k × T0 × (G1 + G2 + ...)))

where R is the output resistance, k=1.380658e-23 J/K is Boltzmann's constant, T0=290 K is the standard noise temperature, G1 is the primary power gain from the input noise frequency to the output noise frequency, and G2+... is the sum of all higher order mixing gains which mix from some input frequency to the output noise frequency. For an amplifier, G2+... is zero under small-signal operation. vn2 / R represents the noise added by the amplifier while k    T0 represents the noise power available from the input termination. In the following, we outline how Amplifier2 calculates noise voltages and noise figures in various cases. This will be compared to the behavior of Amplifier.
 

Small-Signal Operation, NF-Only Mode
Consider an amplifier with NF=5 dB, Z1=25 Ohm and S21=1. The corresponding values of NFmin, Sopt and Rn have been described previously. We will consider the two S11 values S11=0 and S11=0.2. The amplifier lives in an environment where Ys=1/50 Siemens and R=50 Ohm. For this amplifier, the noise figure on the output should be NF=5.356 dB.

Amplifier calculates the noise voltage via:

Doing the numerical evaluations, we get vn=657.93pV. This value is independent of S11. Because the G1 term used in the calculation of NFssb and NFdsb varies with S11, NFssb and NFdsb will vary with S11. Specifically, we get NFssb=NFdsb=5.356 dB for S11=0 (matches NF) and NFssb=NFdsb=4.940 dB for S11=0.2 (does not match NF).

Amplifier2 calculates the noise voltage differently. First, four noise correlation coefficients are calculated via:
< vn , vn > = 4 × k × T0 × Rn
< in , in > = 4 × k × T0 × Rn × |Yopt|2
< vn , in > = 4 × k × T0 × Rn × ((Fmin-1)/(2 × - Rn ) Yopt)
< in , vn > = conj(< vn , in >)

The noise voltage can then be calculated from:

where G is the trans-voltage-gain of the amplifier and Z is the trans-impedance of the amplifier. These can be found from an adjoint circuit analysis of the amplifier and become G=-0.4714 and Z=-23.5702 Ohm for S11=0 and G=-0.5051 and Z=-25.2538 Ohm for S11=0.2. The noise voltage then becomes vn=657.93 pV for S11=0 and vn=704.93 pV for S11=0.2. We see that vn varies with S11; this is not surprising. The noise voltage at the output of the Noisy2Port is independent of S11 but this voltage is passed through the SDD and will see a small-signal gain. NFssb and NFdsb become 5.356 dB independent of S11 (matches NF).
 

Small-Signal Operation, (NFmin, Sopt, Rn) Mode
Consider an amplifier with NFmin=5 dB, Sopt=0.1+j × 0.2, Rn=40, Z1=25 Ohm and S21=1. We will consider the two S11 values S11=0 and S11=0.2. The amplifier lives in an environment where Ys=1/(10-j × 20) Siemens and Zl=30. For this amplifier, the noise figure on the output should be NF=9.520 dB.

In this case, Amplifier2 calculates its noise voltage from the same equations as for NF-only mode. The only difference is the NFmin, Sopt and Rn values used. Amplifier2 produces the noise voltage vn=766.79 pV for S11=0 and vn=749.68 pV for S11=0.2. For both S11 values, this leads to NFssb=NFdsb=9.520 dB. Amplifier calculates noise voltages different from NF-only mode but is again wrong. Amplifier produces the noise voltage vn=611.47 pV for S11=0 and vn597.83 pV for S11=0.2. For both S11 values, this leads to NFssb=NFdsb=7.823 dB.
 

Large-Signal Operation
The above sections present the noise behavior of Amplifier and Amplifier2 in NF-only mode and (NFmin, Sopt, Rn) mode. These apply as the amplifier is operated under small-signal conditions. As the power is increased and the amplifier is operated under large-signal conditions, the expressions for NFssb and NFdsb still apply but some of the terms change.

Consider the expressions for NFssb and NFdsb. These are:
NFssb= 10*log( (vn2 / R + k × T0 × (G1 +G2 +...)) / ( k × T0 × G1))
NFdsb=10*log( (vn2 / R + k × T0 × (G1 +G2 +...)) / ( k × T0 × (G1 + G2 + ...)))

At low powers, G1 is the amplifier's small-signal gain and G2+... is zero. As the power increases and the amplifier compresses, G1 decreases (gain expansion could precede this trend) and G2+... increases. This is a function of the signal properties of the amplifier and is independent of the amplifier's noise model. The variation of G1 and G2+... as a function of the power level is the same for Amplifier and Amplifier2. This is not the case for the noise voltage vn. For Amplifier, vn is constant as the amplifier compresses. For Amplifier2, the noise voltage at the output of the Noisy2Port will pass through the SDD which means that vn decreases as the amplifier compresses. This lowers vn2/R for Amplifier2 relative to Amplifier, causing Amplifier2 to produce smaller noise figures in compression than Amplifier.

Notes/Equations
  1. Amplifier2 is introduced as a replacement for Amplifier. To change an existing Amplifier component to an Amplifier2 component, simply change the name from Amplifier to Amplifier2 on the schematic. The parameters for the two models are the same and Amplifier2 will adopt the values for Amplifier, making parameter re-entry unnecessary. The only exception is that the parameters GainCompType, ReferToInput and ClipDataFile will take their default values LIST, OUTPUT and yes, respectively, regardless of the values these parameters had for Amplifier. Also, the Amplifier display settings will be ignored. Amplifier2 will simply adopt its default settings, displaying S21, S11, S22 and S12.
    For examples of how to use Amplifier2, see the example project examples/Tutorial/Amplifier2_Example_prj or search the ADS examples for designs where Amplifier2 is currently used. To locate such examples, use the ADS documentation Search feature, search in: Examples, and enter Amplifier2. As each found item is highlighted, the ADS examples project directory information is displayed; from the ADS Main window select File > Example Project to navigate to these examples.
    Major Differences between Amplifier and Amplifier2 summarizes the major differences between Amplifier and Amplifier2.
    Major Differences between Amplifier and Amplifier2
    Amplifier Amplifier2
    AM to PM only supported for some magnitude modes AM to PM supported for all magnitude modes
    AM to PM broken AM to PM working
    Non-physical noise behavior Physical noise behavior
    Real/imaginary polynomial fit Magnitude/phase polynomial fit
    Complex S21 leads to non-physical time-domain waveforms Complex S21 leads to physical time-domain waveforms
    For large harmonic balance and circuit envelope simulations Amplifier2 may be slower than Amplifier.
  2. Use the functions polar(mag,ang), dbpolar(dB, ang), or VSWRpolar(VSWR, ang) to convert the Sij specifications into complex numbers. Note that Sij are voltage gains and not power gains. For example, an amplifier with S21=polar(10,0) and S11=S22=S12=0 will scale the voltage by a factor of 10 from input to output and will therefore result in a 20 dB increase in power. S21=dbpolar(10,0), on the other hand, will result in a 10 dB increase in power.
  3. For an S-parameter or a noise figure sinusoidal ripple, use the function ripple (mag, intercept, frequency, variable); for example ripple(0.1, 0, 10 MHz, freq).
    example: S21=dbpolar(10.0+ripple(0.1,0,10MHz,freq),0.0)
  4. When defining gain using S21, remember that this gain is applied to the forward incident wave into the input of the amplifier. This is in keeping with the measurement standards used to define amplifier gain at the system level. This means that if we change S11 from 0 to 0.9 for example, we will see no change in output power because the reflected wave is not taken into account by the amplifier's definition of gain, only the incident wave.
  5. Amplifier2 behaves differently from Amplifier for complex S21 values. The phase shift is applied before the nonlinear polynomial instead of after, leading to much more realistic waveforms. To see this, consider for example an Amplifier and Amplifier2 with S21=dbpolar(10,50), TOI=20 dBm, GainCompPower=10 dBm and GainComp=2 dB. Excite and terminate these with default P_1Tone and Term components and carry out a high-order harmonic balance analysis, say Order=150, at a high input power, say 30 dBm. Because the amplifiers are excited with a sine wave and operate deep into compression, we expect the output time domain waveform to be clipped and closely resemble a square wave. Except for the expected differences at transitions where the effect of a finite Order is evident, this is the case for Amplifier2 but is not at all the case for Amplifier.
  6. Z1 and Z2, the reference impedance parameters for ports 1 and 2, are used in conjunction with the parameters S11/S21/S12/S22. This is because S-data is always used with respect to a particular reference impedance.
  7. Amplifier2 does not support complex reference impedances.
  8. Amplifier2 passes dc.
  9. For circuit envelope simulation, baseband signals are blocked.
  10. Amplifier2 may be slower than Amplifier for large harmonic balance and circuit envelope simulations.
  11. Modeling Basics presented the polynomial model used for modeling the output voltage as a function of the input voltage. It also presented the result of pushing an A1 × cos(ω1 × t)+ A2 × cos(ω2 × t) signal through ay=a1 × x + a2 × x2 + a3 × x3 nonlinearity. Based on this, we can calculate the IP2 (second-order intercept) and IP3 (third-order intercept) of the amplifier. The general equation for the nth-order intercept point IP n is IP n=(n × P1-Pn)/(n-1) where P1 is the power level of the first-order tone and Pn is the power level of the nth-order tone.
    The Pn power level, however, is not unique. Look at the amplifier output. Ignoring A1 and A2 which we can normalize out, the second-order harmonics cos(2 × ω1 × t) and cos(2 × ω2 × t) have the amplitude 1/2 × a2 while the second-order intermods cos((ω1-ω2) × t) and cos((ω1+ω2) × t) have the amplitude a2. Similarly, the third-order harmonics cos (3 × ω1 × t) and cos(3 × ω2 × t) have the amplitude 1/4 × a3 while the third-order intermods cos((2 × ω1+ω2) × t), cos((2 × ω1-ω2) × t), cos((2 × 2ω+1ω) × t) and cos((2 × ω2-ω1) × t) have the amplitude 3/4 × a3. If the formula IP n = (n × P1-Pn)/(n1) works for one type of second and third-order tone, it will not work for the other.
    The industry standard definitions of IP2 and IP3 are based on intermods, not harmonics. When polynomial coefficients are determined in the Amplifier2 code, they are therefore based on intermods. When validating Amplifier2 using intermods, everything checks out; when using harmonics, it does not. This shows that we cannot validate the proper SOI and TOI for Amplifier2 using a one-tone analysis because this generates only harmonics but not intermods. We use industry standard definitions when deriving the coefficients for Amplifer2 and it is imperative to do the same when validating Amplifier2.
    Note that SOI and TOI are defined at a low power level. If SOI and TOI are calculated at a power level where either P1 or Pn deviate from their low-power values, the results will be in error. To see this, sweep the input power and plot the IP3 of the Amplifier2 as a function of the input power. At low powers, the IP3 of the amplifier will match the TOI parameter set on the Amplifier2. Amplifier2 was constructed to have the TOI parameter as its IP3 at low powers so this is expected. As the input power increases, IP3 will start to deviate from the TOI value for low input powers. This simply reinforces the importance of calculating IP3 at low input powers. Too high, and IP3 changes. Note that it is not enough that the fundamental tone varies linearly. SOI/TOI is calculated based on the fundamental and the second/third-order intermod so one must ensure that the second/third-order intermods are also linear or SOI/TOI will change.
    Note also that Amplifier2 must be output impedance matched in order for the SOI/TOI validation to check out.
  12. The common expectation for the behavior of the adjacent channel power rejection (ACPR) for an amplifier operating in compression can be formulated in many equivalent ways: the ACPR decreases/improves as TOI increases; the ACPR decreases/improves as the amplifier becomes more linear; the ACPR decreases/improves as we move away from compression; the ACPR increases/worsens as TOI decreases; the ACPR increases/worsens as the amplifier becomes more nonlinear; the ACPR increases/worsens as we move towards compression.
    This expectation is correct for an amplifier operating linearly. For an amplifier operating in compression, the validity of this expectation depends on the amplifier. We will discuss two cases, a transistor-level amplifier and a polynomial amplifier.
    The expectation may or may not be correct for a transistor-level amplifier operating in compression. A transistor-level simulation of a particular amplifier in ADS shows that this expectation holds at some input power ranges but not at others.
    The expectation is incorrect for a polynomial amplifier operating in compression. Modeling Basics presented how two tones react when pushed through a polynomial amplifier and offered a discussion of this analysis. The result is that the large-signal gain will always exceed the small-signal gain. Applied to ACPR skirts, this means that a polynomial amplifier will actually produce a decreasing/better ACPR level as we move further into compression. This may be counter-intuitive but Amplifier2 reacts the way we can theoretically predict that a polynomial amplifier must act. Amplifier2's behavior is simply a function of the polynomial modeling on which it is based.
  13. An S2D file typically consists of an ACDATA block containing small-signal information and a GCOMP i block (i=1, ... , 7) containing compression information. For Amplifier2, the ACDATA block is ignored and the S-parameters specified on the Amplifier2 component are used. If the S-parameters of the ACDATA block must be used, use the AmplifierS2D component instead. Similarly, any NDATA blocks containing noise data are ignored by Amplifier2.
  14. When an S2D file contains gain compression data at more than one frequency, the GainCompFreq must be set to one of the frequencies in the S2D file to identify the data to be used. It is imperative that GainCompFreq be set to one of the frequencies in the S2D file as no interpolation or extrapolation between gain compression data at different frequencies can be performed. For further details regarding GainCompFreq selectivity, refer to Using GCFreq to Resolve GCOMP7 Frequency Conflicts in the AmplifierS2D documentation.
  15. When an S2D file has a power range that exceeds that of a simulation, a choice must be made for the power range used for fitting. Assume an S2D file covers -30 dBm to 30 dBm but that a simulation is carried out from -10 dBm to 10 dBm. In this case, a choice must be made as to whether the polynomial fitting of S2D data is done over the power range -30 dBm to 30 dBm or -10 dBm to 10 dBm. In the former case, the fitting may be inaccurate as the polynomial must cover a large power range that could hold a lot of variations. This is undesirable. However, the advantage of this approach is that the results we get when simulating from -10 dBm to 10 dBm are a subset of what we would have gotten in that interval had we simulated from -30 dBm to 30 dBm. In the latter case, the fitting is much more accurate as the fitting is done over a much smaller power range which presumably holds a lot less variation. This is desirable. However, the problem with this approach is that the results between -10 dBm and 10 dBm will be different for a simulation done from -30 dBm and 30 dBm rather than from -10 dBm and 10 dBm because the polynomial coefficients change as we change the power range of the simulation. ADS does the former. It fits a polynomial to the whole S2D file, not just the subset for which the simulation is carried out. To change the fitting in a power range, it is not enough to change the power range of the simulation. To change the fitting, one must modify the S2D file. The S2D file power range, not the simulation power range, dictates the fitting power range. This is relevant in the following where we discuss different fittings in different power ranges.
  16. A typical Pout (output power) vs. Pin (input power) curve consists of a linearly increasing region, a transition region and a saturation region. Another way of thinking of this is that typical Pout-Pin vs. Pin curve consists of a flat region, a transition region and a linearly decreasing region.
    When the saturation region is made larger and larger, the fitting approach adopted by Amplifier2 (polynomial fitting, odd order terms, order dependent upon the number of data points in the S2D file, max order 9) will tend to produce fitted curves which ring/oscillate more and more at higher powers. Mild ringing is often tolerable and might not even be noticed but if the transition region becomes too large it can make the results useless. To alleviate the problem, reduce the size of the saturation region to the minimum needed and leave no extra points in the S2D file. If the results are still not satisfactory, ensure ClipDataFile is set to yes and reduce the saturation region even more, relying on Amplifier2 extrapolation. If the results are still not satisfactory, try breaking the S2D file into two files and simulate the problem in two steps. Another alternative is to use the AmpSingleCarrier model. This model is based on linear interpolation instead of curve fitting and will not have this ringing problem. AmpSingleCarrier, however, will not produce harmonics. Refer to the AmpSingleCarrier documentation for details.
    If fitted results do not accurately match the data in the S2D file and it is uncertain if this ringing problem is the cause, the problem is very easy to exaggerate. Simply extend the GCOMP7 block of the S2D file with a large flat region (more input powers, saturated output power, saturated output phase) and re-simulate. If the ringing problem is the cause, the results should get worse.
  17. The S2D file capability is a legacy from OmniSys. OmniSys used GComp1-GComp7 data items for specifying gain compression. Gain Compression Data for OmniSys and ADS summarizes the gain compression data for OmniSys and ADS. Refer to OmniSys Parameter Information for OmniSys parameter information. GComp1-GComp6 can be specified by using the corresponding ADS gain compression parameters and setting GainCompType=LIST or they can be contained in an S2D format setting GainCompType=FILE.

    OmniSys

    ADS

    GComp1: IP3

    TOI

    GComp2: 1dBc

    GainComp=1dB

    GComp3: IP3, 1dBc

    TOI

    GComp4: IP3, Ps, GCS

    TOI

    GComp5: 1dBc, Ps, GCS

    GainComp=1dB

    GComp6: IP3, 1dBc, Ps, GCS

    TOI

    GComp7

    GainCompType=FILE


    OmniSys Parameter Information
  18. The GainRF component is the Ptolemy equivalent of the Analog/RF Amplifier2 component. Both of these components are based on the OmniSys legacy (refer to note 16) and the OmniSys cases GCOMP1 through GCOMP7 are shared by GainRF and Amplifier2. For GCOMP1 through GCOMP6 corresponding to GainCompType=LIST, the curve fitting algorithms for GainRF and Amplifier2 are very similar and close results can be expected. However, the curve fitting algorithms are not identical and the shape of the knees of the compression curves will therefore differ slightly. Also, the levels at which the various fundamentals saturate can be different. These levels will generally differ more when Psat is not set than when Psat is set. For GCOMP7 corresponding to GainCompType=FILE, the curve fitting algorithms for GainRF and Amplifier2 are different and different results can be expected.
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