An Integrated Overview of CAD/CAE Tools and Their Use on Nonlinear Network Design

Transcription

1 An Integrated Overview of CAD/CAE Tools and Their Use on Nonlinear Networ Design José Carlos Pedro and Nuno Borges Carvalho Telecommunications Institute University of Aveiro International Microwave Symposium /6 Summary Objectives The Nonlinear RF Networ CAD Problem Methods for Nonlinear RF Circuit and System Simulation Nonlinear Device and Circuit Modeling 5 Design Validation 6 Conclusions International Microwave Symposium /6

2 Objectives - Present an overview of the various CAD tools for RF/microwave nonlinear networ design. - Integrate some fields held in nonlinear circuit/system design, as: - nonlinear circuit and device modeling strategies, - nonlinear circuit/system analysis methods valid for RF design - circuit performance evaluation and design validation International Microwave Symposium /6 Summary Objectives The Nonlinear RF Networ CAD Problem Methods for Nonlinear RF Circuit and System Simulation Nonlinear Device and Circuit Modeling 5 Design Validation 6 Conclusions International Microwave Symposium /6

3 The Nonlinear RF Networ CAD Problem - v(t) V() V() V() V() t DAC 9 DAC v(t) Osc ocal t No closed-form solutions are possible! CAD tools, are necessary. And so are accurate mathematical modeling of devices, circuits and signals. International Microwave Symposium 5/6 The Nonlinear RF Networ CAD Problem - Signals which are Envelope Modulated RF Carriers: v(t) S() t Aperiodic of Continuous Spectra and involving Time-scales?? An approximate signal model is required! International Microwave Symposium 6/6

4 The Nonlinear RF Networ CAD Problem - Approximate Models for Envelope Modulated RF Carriers S() Sinusoidal: V() Two-Tone: V() V() V() Multi-Tone: International Microwave Symposium 7/6 The Nonlinear RF Networ CAD Problem - Approximate Models for Envelope Modulated RF Carriers Time-Varying RF Carrier: j ( ) e τ τ V i S (t) i Se (τ ) i Sc (τ ) t τ τ I s ( c,τ )... or simply represent and simulate only the envelope!... c τ International Microwave Symposium 8/6

5 Summary Objectives The Nonlinear RF Networ CAD Problem Methods for Nonlinear RF Circuit and System Simulation Nonlinear Device and Circuit Modeling 5 Design Validation 6 Conclusions International Microwave Symposium 9/6 Methods for Nonlinear RF Circuit and System Simulation - Nonlinear RF Networ Modeling Tae, for example, this Nonlinear Networ: i S (t) v O (t) q N [v O (t)] i N [v O (t)] It can be represented by the following ordinary differential nodal equation: [ v ( t) ] d q v ( t) N O O in O = S t d t [ v ( t) ] i ( ) International Microwave Symposium /6 5

6 Methods for Nonlinear RF Circuit and System Simulation - Time-Step Integration [ v ( t) ] d q v ( t) N O O in O = S t d t [ v ( t) ] i ( ) This ODE is solved for v O (t) transforming it into a difference equation, discretizing time in various instants t separated by dynamic steps h : or [ v ( t )] q [ v ( t )] q v ( ) N O N O O t in O = S h [ v ( t )] i ( t ) [ v ( t )] h i [ v ( t )] = h i ( t ) q [ v ( t )] h vo ( t ) qn O N O S N O which is then solved in a time-sep by time-step basis, for all v O (t ), beginning with the initial state v O (t ) until final time v O (t K ). International Microwave Symposium /6 Methods for Nonlinear RF Circuit and System Simulation - Time-Step Integration Since this time-step integration scheme was conceived for transient response calculations it is: - Inefficient: Steady-State response requires waiting until all transients died. - Inadequate: Wors on time-domain while most signal and circuit models, are represented in frequency-domain. - Inaccurate: Impossibility of waiting for complete vanishing of long transients, as use of the DFT between domains introduce large errors. Nevertheless, time-step integration is still one of the mostly used methods of nonlinear circuit and system simulation!! It is the core method of all SPICE lie or Simulin programs. International Microwave Symposium /6 6

7 Methods for Nonlinear RF Circuit and System Simulation - Time-Domain Calculation of Steady-State Responses ( Shooting Newton ) To bypass the transient computation, the initial condition, v O (t ), must be selected such that after the excitation period T the same initial state is obtained: vo ( t T ) = vo ( t) for is ( t T ) = is ( t) The idea is to estimate the sensitivity of the final state, v O (t T), to variations in the initial condition, v O (t ) : S [ v ( t )] O vo ( t T ) vo ( t) v O vo ( t T ) ( t ) vo ( t) and then use this sensitivity to propose an educated guess for the correct initial condition v O (t ). International Microwave Symposium /6 Methods for Nonlinear RF Circuit and System Simulation - 5 Time-Domain Calculation of Steady-State Responses ( Shooting Newton ) In the Shooting-Newton algorithm, this sensitivity, S[v O (t )], is used to iteratively solve the boundary-value nonlinear equation: vo ( t T ) = vo ( t) or vo ( t T ) vo ( t) = determining the new initial condition estimate, i v O (t ), from i v O (t ), and the result of a time-step integration in a period, i v O (t T), by: { S[ i v ( t )] }. [ i v ( t T ) i v ( t )] i v ( t ) i O = vo ( t) O O O Shooting-Newton is an interesting alternative for RF steady-state simulation as S[ i v O (t )] can be obtained along with time-step integration without any postprocessing, and because it seems that the boundary-value equation v O (t T)- v O (t )= is mildly nonlinear, although the circuit may be strongly nonlinear. International Microwave Symposium /6 7

8 Methods for Nonlinear RF Circuit and System Simulation - 6 Frequency-Domain Methods The RF approach for analyzing our circuit is to treat it in frequency-domain: i S (t) v O (t) q N [v O (t)] i N [v O (t)] Both the excitation and the state-variables are represented as truncated Fourier series: K K j t is ( t) = I s e and j t v = O( t) Vo e =K =K which, substituted in the circuit s time-domain ODE gives: [ v ( t) ] d q v ( t) N O O in O = S t d t d dt [ v ( t) ] i ( ) j t j t j t V o qn V e o e in V o e = j t I s e International Microwave Symposium 5/6 Methods for Nonlinear RF Circuit and System Simulation - 7 Frequency-Domain Methods d dt j t j t j t V o qn V e o e in V o e = j t I s e Because terms of Fourier series are orthogonal, this actually corresponds to a nonlinear system of (K) equations, one for each harmonic component. In matrix form, that system is nown as the armonic-balance Equation. ( Vo ) Inl ( Vo ) Is V o jωqnl = International Microwave Symposium 6/6 8

9 Methods for Nonlinear RF Circuit and System Simulation - 8 Frequency-Domain Methods ( Vo ) Inl ( Vo ) Is V o jωqnl = There are two alternative ways of solving this B equation for V o : In Volterra Series it is assumed that the problem is only mildly nonlinear, and so that its solution can be approximated by the analytical solution of a similar problem in which the nonlinearities are approximated by low order Taylor series expansions. In armonic-newton, the full nonlinear B equation is iteratively solved using a multi-dimensional Newton-Raphson algorithm. International Microwave Symposium 7/6 Methods for Nonlinear RF Circuit and System Simulation-9 Volterra Series Approximating q N [v O (t)] and i N [v O (t)] by low order Taylor series expansions around the quiescent point, (I S,V O ), the nonlinear charge and current signal components can be given by: ( ) vo c vo ( t) cvo( t) cvo ( t) ( ) and i v g v ( t) g v ( t) g v ( t qnl nl o o o o ) which leads to a circuit solution v o (t) of the form: Q Q j( q ) t vo( t) = I n Sq I qn Sq n n( q,, q ) e n n= q = Q qn = Q In Volterra Series the system becomes completely identified by its Nonlinear Transfer Functions. Volterra series can thus be applied to either Circuit or System Analysis and Design! International Microwave Symposium 8/6 9

10 Methods for Nonlinear RF Circuit and System Simulation - Volterra Series () v o (t) () A () v o (t) i S (t) B () X (, ) v o(t) A () v o (t) B () X C () (,, ) International Microwave Symposium 9/6 Methods for Nonlinear RF Circuit and System Simulation - armonic-newton Alternatively, the full nonlinear harmonic-balance equation ( Vo ) Inl ( Vo ) Is V o jωqnl = can be solved for V o using a (K)-dimensional Newton-Raphson algorithm. When the B equation is put in the form: F ( V ) V jωq ( V ) I ( V ) I = o o nl o nl o s the solver creates a succession of solution estimates V o, V o,..., i V o, i V o,..., f V o until F( f V o ) < ε. i i df Vo = Vo d V o ( V ) o F( i V ) i Vo = Vo o International Microwave Symposium /6

11 Methods for Nonlinear RF Circuit and System Simulation - armonic-newton The armonic-newton is the most used method for microwave circuit simulation. In the Piecewise armonic-newton implementation, the networ i S (t) v O (t) q N [v O (t)] i N [v O (t)] International Microwave Symposium /6 Methods for Nonlinear RF Circuit and System Simulation - armonic-newton The armonic-newton is the most used method for microwave circuit simulation. In the Piecewise armonic-newton implementation, the networ is divided into two sub-circuits, one nonlinear, memoryless, and another linear, dynamic, which, with the excitation, allow the construction of a nodal form of the B equation: i C (t) I cl () I cnl ()=DFT[i CN (t)] I s () V o () d dt { q } N [v O (t)] i N [v O (t)] where F ( V ) I ( V ) I ( V ) I ( ) = o cl ( V ) ( ) V ( ) I cl o = Y cl o o and cnl o Icnl s { [ ]} ( ) V = DFT i DFT [ V ( ) ] o CN o International Microwave Symposium /6

12 Methods for Nonlinear RF Circuit and System Simulation - Multi-Rate Techniques When the excitation is an RF carrier cos( t) modulated by a base-band envelope v e (t), which is uncorrelated with that carrier, the circuit behaves as if it had a stimulus dependent on two different time-scales τ and τ : i S ( τ, τ) = Ve ( τ)cos( τ ) The, circuit s ODE, in t: dq [ v ( t) ] v ( t) N O O in dt O = S t [ v ( t) ] i ( ) becomes a Multi-Rate Partial Differential Equation, MPDE, in (τ,τ ): [ v ( τ, τ )] q [ v ( τ, τ )] q v ( τ, ) τ N O N O O in O = S τ τ τ [ v ( τ, τ )] i ( τ, ) which again can be solved in a bi-dimensional time-domain for v O (τ,τ ), or bidimensional frequency-domain for V o ( Ω, ). International Microwave Symposium /6 Methods for Nonlinear RF Circuit and System Simulation - Multi-Rate Techniques If both the envelope and the carrier are periodic, then it is probably better to solve the MPDE is frequency-domain. In this case, the state variable would become: vo ( τ, τ ) which substituted in the MPDE: = V, e jω τ e j τ [ v ( τ, τ )] q [ v ( τ, τ )] q v ( τ, ) τ N O N O O in O = S τ τ τ [ v ( τ, τ )] i ( τ, ) would lead to the following bi-dimensional B equation, the basis for most of the multi-tone nonlinear simulation methods.. Vo ( Ω, ) Inl[ Vo ( Ω, )] jω Qnl[ Vo ( Ω, )] Is( Ω, ) = International Microwave Symposium /6

13 Methods for Nonlinear RF Circuit and System Simulation - 5 Multi-Rate Techniques In most practical cases, however, the envelope is aperiodic, and so it is better to solve the MPDE in the frequency-domain,, for the carrier, but in the timedomain, τ, for the envelope. In this case, the state variable would become: j = τ v (, ) O τ τ V ( τ ) e which substituted in the MPDE would lead to the following τ time-varying B equation: [ V ( τ )] Q V ( τ ) nl o o jωqnl o nl o s τ = τ [ V ( τ )] I [ V ( τ )] I ( ) International Microwave Symposium 5/6 Methods for Nonlinear RF Circuit and System Simulation - 6 Multi-Rate Techniques This time-varying B equation is now discretized in τ -time [ V ( τ )] Q [ V ( τ )] Q V ( ) nl o nl o o τ jωqnl o nl o s = h [ V ( τ )] I [ V ( τ )] I ( τ ) which allows the determination of the envelope transient solution for each of the V o (τ ) harmonics, solving: [ V ( τ )] j h ΩQ [ V ( τ )] h I [ V ( τ ]= h Vo ( τ ) Qnl o nl o nl o ) [ V ( τ )] = h Is( τ ) Qnl o This method, nown as Envelope Transient armonic-balance, constitutes a serious step towards a true nonlinear system envelope simulator. International Microwave Symposium 6/6

14 Methods for Nonlinear RF Circuit and System Simulation - 7 In summary, this envelope transient harmonic-balance can be described by: º - Represent the excitation as an RF carrier modulated by a base-band envelope: i S (t) i Se (τ ) i Sc (τ ) t τ τ or, in-frequency: I s () I s (Ω) I s ( c ) Ω * - c c c International Microwave Symposium 7/6 Methods for Nonlinear RF Circuit and System Simulation - 8 º - Discretize the base-band envelope at instants τ, create the excitation at those instants I s (τ ), and calculate the solution, V o (τ ), by an armonic- Newton solver. º - Interpolate the obtained V o (τ ) variations. i Se (τ ) I s ( c,τ ) V o ( c,τ ) V o ( c,t e ) c c c τ τ τ International Microwave Symposium 8/6

15 Methods for Nonlinear RF Circuit and System Simulation - 9 º - Finally, reconstruct the solution in frequency, V o (), and time-domains v O (t). V o (Ω) V o ( c ) Ω * V (Ω) V ( c ) c V o () v O (t) Ω * - c c c V o (Ω) V o ( c ) = t Ω * - c c c V o (Ω) V o ( c ) Ω * - c c c International Microwave Symposium 9/6 Summary Objectives The Nonlinear RF Networ CAD Problem Methods for Nonlinear RF Circuit and System Simulation Nonlinear Device and Circuit Modeling 5 Design Validation 6 Conclusions International Microwave Symposium /6 5

16 Nonlinear Device and Circuit Modeling - Correct design of nonlinear networs demands for a precise description of the whole circuit, which includes the nonlinear active device, but also matching and bias networs. Circuit Modeling V VD RF In RF Out Nonlinear Device Modeling International Microwave Symposium /6 Nonlinear Device and Circuit Modeling - Frequency modeling of the matching circuits is usually undertaen for the fundamental and, when the goal is efficiency or distortion, for the harmonics. Bias networs are usually neglected Typical microwave/millimeter wave networ analyzers are only capable of measuring S parameters above Mz, while envelopes span up to a few hundreds of Kz or Mz, at most!... International Microwave Symposium /6 6

17 7 /6 International Microwave Symposium A simple Volterra model shows the impact of all in-band and out-of-band terminating impedances. Nonlinear Nonlinear Device Device and and Circuit Circuit Modeling Modeling - ( ) ( ) ds m = ( ) ( ) ( ) ( ) [ )] ( ) ( ) ( ) ( ) ( ) (, d md md m ds = ( ) ( ) ( ) ( ) ( ) ( ) ( ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )),, 6,, ,, md md d m d m md md d d d m ds = Fundamental Base-Band Fundamental nd armonic /6 International Microwave Symposium E.E5.E6.E7.E8.E9 Tone Separation [z] Asymmetry [db]..5 j. -j. j.5 -j.5 j -j f-z (Mz) dbm Base-band, and/or, bias networs are usually ignored by the designer, although they can be of paramount importance in nonlinear networ design. They control signal s envelope dynamics, e.g. manifested as IMD asymmetries! Nonlinear Nonlinear Device Device and and Circuit Circuit Modeling Modeling -

18 Nonlinear Device and Circuit Modeling - Base-band, and/or, bias networs are usually ignored by the designer, although they can be of paramount importance in nonlinear networ design. They control signal s envelope dynamics, e.g. manifested as IMD asymmetries! - j.5 j - dbm - j j f-z (Mz) 8 6 -j.5 -j Asymmetry [db] E.E5.E6.E7.E8.E9 Tone Separation [z] International Microwave Symposium 5/6 Nonlinear Device and Circuit Modeling - Base-band, and/or, bias networs are usually ignored by the designer, although they can be of paramount importance in nonlinear networ design. They control signal s envelope dynamics, e.g. manifested as IMD asymmetries! - j.5 j - dbm - j j f-z (Mz) 8 6 -j.5 -j Asymmetry [db] E.E5.E6.E7.E8.E9 Tone Separation [z] International Microwave Symposium 6/6 8

19 Nonlinear Device and Circuit Modeling - Base-band, and/or, bias networs are usually ignored by the designer, although they can be of paramount importance in nonlinear networ design. They control signal s envelope dynamics, e.g. manifested as IMD asymmetries! - j.5 j - dbm - j j f-z (Mz) 8 6 -j.5 -j Asymmetry [db] E.E5.E6.E7.E8.E9 Tone Separation [z] International Microwave Symposium 7/6 Nonlinear Device and Circuit Modeling - 5 Real telecommunication signals involve envelopes of dense spectrum. Bias networs must be accurately represented from DC to Envelope Bw. All this bandwidth is accounted for j.5 j - - j. -5 Pout [dbm] j. -8 -j.5 -j Frequency-fcentral K[z] International Microwave Symposium 8/6 9

20 Nonlinear Device and Circuit Modeling - 6 Nonlinear Device Model Formulation Any transistor, which is a memoryless nonlinearity embedded in a linear dynamic networ becomes: a complex dynamic nonlinear device if tested on its terminals, S v S v Dynamic Nonlinear Two-Port v v - - International Microwave Symposium 9/6 Nonlinear Device and Circuit Modeling - 7 Nonlinear Device Model Formulation Any transistor, which is a memoryless nonlinearity embedded in a linear dynamic networ becomes: a complex dynamic nonlinear device if tested on its terminals, or a memoryless nonlinearity if deembedded from its linear dynamic elements. v S S Memoryless Nonlinear v v Two-Port v - - i =f (v, v ) i =f (v, v ) - v - v Dynamic inear Four-Port [Y] x International Microwave Symposium /6

21 Nonlinear Device and Circuit Modeling - 8 Nonlinear Device Model Formulation For illustrative purposes, we will now discuss a Nonlinear MESFET Model obtained using the above procedure. First step is to adopt a certain equivalent circuit topology, identifying there the nonlinear elements and the embedding dynamic networ Rg g Cgd Cgs d Rd Ccg Cpg Ccd Cds Ri i DS (v S,v DS ) D s Rs S International Microwave Symposium /6 Nonlinear Device and Circuit Modeling - 9 Nonlinear Device Model Formulation In the MESFET case, we used one-dimensional physics simulations of the device to get detailed information on the i DS (v S,v DS ) and Cgs(v S ) functions. The adopted functions are valid in a large range of v S and v DS, are continuous and present continuous derivatives, and approximate reasonably well the measurements at least up to the rd derivative. ids ( vs, vds ) = β [ u u u ln( e e )] tanh( α v ) DS They are thus consistent with measured ( order) DC, (st order) S-par, and (nd and rd order) harmonic distortion. International Microwave Symposium /6

22 Nonlinear Device and Circuit Modeling - Nonlinear Device Model Extraction The linear equivalent circuit was extracted from small-signal frequency swept S-parameter data, using the direct method of Dambrine et al, and then adjusted by careful linear optimization. i DS (v S,v DS ) nonlinear model parameters were extracted by comparing measured I DS, and all its first 9 derivatives up to order in respect to v S and v DS, ids ( vs, vds ) IDS mvgs dsvds mvgs md vgs vds dvds mv gs m d vgs vds md vgs vds d vds with the ones predicted by the adopted functional description. International Microwave Symposium /6 Nonlinear Device and Circuit Modeling - The derivatives extraction procedure is based on intermodulation measurements when the device is excited at its input and output by one tone at, and another one at. V S and V DS Power Supply V S V DS Spectrum Analyzer Diplexer Diplexer 5Ω oad ATTN PF D.U.T PF ATTN V S ( ) V ( ) International Microwave Symposium /6

23 Nonlinear Device and Circuit Modeling - As seen in the figures, i DS (v S ) derivatives predicted by the model are in very good agreement with correspondent measured data Ids, m, m, m [mu].. -. m Meas m Meas Ids, m, m, m [mu].. -. m Model m Model -. m Meas Ids Meas -. m Model Ids Model Vgs [V] Vgs [V] Measured and modeled drain source current, i DS, and its derivatives, m, m and m International Microwave Symposium 5/6 Nonlinear Device and Circuit Modeling - The same set-up can also be used for extracting Cgs(v S ) coefficients. But now, higher frequencies must be applied. Spectrum Analyzer V S and V DS Power Supply V S V DS Diplexer Diplexer ATTN PF D.U.T 5Ω oad 5Ω oad V S ( ) International Microwave Symposium 6/6

24 Nonlinear Device and Circuit Modeling - Cgs(v S ) and its derivatives predicted by the model are again in a reasonable good agreement with correspondent measured data..8.6 Cgs Meas Cg Meas Cg Meas.5.. Cgs, Cg, Cg [pu].. Cgs, Cg, Cg [pu] Vgs [V] -. Cgs Model Cg Model Cg Model Vgs [V] Measured and modeled gate source capacitance, and its derivatives Cgs, Cg, and Cg International Microwave Symposium 7/6 Nonlinear Device and Circuit Modeling - 5 An alternative way to this device and circuit level modeling is System or Blac-Box Behavioral Modeling Conceived for the efficient simulation of large telecommunication systems, it tries to find input/output transfer functions that accurately describe the observed responses of the system. At the present time it seems we can model exactly mildly nonlinear dynamic systems by Volterra series, and we could also model strong nonlinear memoryless systems, but we can not yet represent strong nonlinear dynamic systems. Presently an important effort is being paid to solve this challenging problem! International Microwave Symposium 8/6

25 Summary Objectives The Nonlinear RF Networ CAD Problem Methods for Nonlinear RF Circuit and System Simulation Nonlinear Device and Circuit Modeling 5 Design Validation 6 Conclusions International Microwave Symposium 9/6 Design Validation - The simplest approach to nonlinear networ design validation is testing under a sinusoidal excitation: y(t) = A cos(t) V( ) the output is nothing but the sum of a DC component, the fundamental and its harmonics: y() International Microwave Symposium 5/6 5

26 Design Validation - Only gain compression (AM/AM) and phase shift (AM/PM) versus input power, can be verified. Exclusively accounts for short memory effects at the fundamental frequency. ain [db] Input Power [dbm] Phase Change [º] Input Power [dbm] Can not account for the envelope or signal bandwidth behavior! International Microwave Symposium 5/6 Design Validation - Testing for simple envelope effects requires, at least, a two-tone excitation: envelope V ( ) V ( ) x( t) = Ai cos( t ) Ai cos( t) = Ai cos t cos t y( t) = a A a A cos i 9 aai aai sin a Ai cos aai sin aai sin a Ai sin i [( ) t] ( t) a A a A sin( t) i ( t) a A cos[ ( ) t] cos( t) [( ) t] a A sin[ ( ) t] i [( ) t] a A sin[ ( ) t] sin( t) ( t) i i i i 9 i a A carrier a A International Microwave Symposium 5/6 6

27 time [s] Design Validation - Since the envelope of a two-tone signal is a pure sinusoid, these tests are actually sensing the nonlinear networ s long-term memory effects only at specific frequency spots. Specific tone separation V ( ) V ( ) j.5 j envelope j...5 -j. Amplitude -j.5 -j International Microwave Symposium 5/6 Design Validation - 5 To account for multi-frequency envelopes, multi-tone excitations are needed: K y( t) = A cos t θ = ( ) V() Deterministic Multi-Tone The output spectrum spans through many tone-clusters located at the base-band, the fundamental and the various harmonics. Amplitude [U] BaseBand RF RF RF International Microwave Symposium 5/6 7

28 Design Validation - 6 Special care should be paid to the phase arrangements of multi-tone signals as they define envelope pea-power, and thus strongly affect nonlinear response. Amplitude Amplitude time time Time waveform representation of two signals composed of evenly spaced and equal amplitude tones, but with different phase arrangements. International Microwave Symposium 55/6 Design Validation - 7 Best results are obtained using the signals which the system is intended to handle. But, these signals are sometimes substituted by RF band-limited gaussian noise. SM excitation (in frequency and time) CDMA excitation (in frequency and time) International Microwave Symposium 56/6 8

29 Design Validation - 8 To illustrate those design validation ideas let us compare simulation and measured results obtained with a practical MESFET microwave amplifier. V VD RF In RF Out International Microwave Symposium 57/6 Design Validation - 9 This amplifier was modeled as previously explained, and then tested under Two-Tone excitation. A perfect match between B simulations and measurements is evident... Output Power [dbm] Measured Pout (w) Measured IMD (w-w) Simulated IMD (w-w) Simulated Pout (w) Measured Pout (w) Measured IMD (w-w) Simulated IMD (w-w) Simulated Pout (w) Input Power [dbm] International Microwave Symposium 58/6 9

30 Design Validation - Finally, the amplifier was tested for a Band-imited White Noise excitation. The stimulus power spectral density was: Input Power [dbm] Frequency-Fcentral [Kz] Power spectral density function of the noise stimulus. International Microwave Symposium 59/6 Design Validation - Measured and B simulated in-band output results of ACPR and CCPR are depicted in the figure. Once again, a very good agreement was obtained between both data types Measured CCPR Measured Output Power Simulated Output Power Simulated CCPR -5 Pout [dbm] Freq-z [dbm] Power spectral density function of the amplifier s in-band output. This proves the enormous benefits of the present CAD tools in nonlinear microwave networ design. International Microwave Symposium 6/6

31 Summary Objectives The Nonlinear RF Networ CAD Problem Methods for Nonlinear RF Circuit and System Simulation Nonlinear Device and Circuit Modeling 5 Design Validation 6 Conclusions International Microwave Symposium 6/6 Conclusions - Although nonlinear networ design is a problem of complex nature, it is rapidly advancing towards a mature state. Because both short-term and long-term memory effects are involved, simulating nonlinear networs subject to telecommunication signals requires efficient mixed-mode multi-rate techniques. International Microwave Symposium 6/6

32 Conclusions - But, it also requires specific electron device and terminating networs modeling, valid, not only near the excitation frequency, as at the base-band and the first few harmonics. Because the response of a nonlinear networ to a certain input can not be determined from the response to any other excitation, it must be tested with signals as close as possible to the expected real ones. owever, it seems that reasonable design analysis and validation can already be obtained from band-limited noise approximations. International Microwave Symposium 6/6