.Under this hypothesis, the output current waveform is forced by the device itself (i.e. through the input driving signal), while the output voltage is properly shaped through the selection of suitable harmonic terminations 13, 16, 17. Moreover, after a critical review of the classical approach (based on an ideal waveform shaping), the implementation of microwave Class F amplifiers will be discussed, clarifying the role of the device bias and its loading conditions. Among such approaches, the Class F technique has gained popularity, thanks to its particular features, including higher efficiency and output power performance if compared to quasi-linear approaches (i.e. Class A or Class B). Furthermore, such performance is accomplished via a modest and acceptable increase in output matching network complexity, arising from the need to impose a suitable output loading, not only at fundamental but also at harmonic frequencies of the input signal. Moreover, expressions (5.59) and (5.61) easily quantify the improvements in power performance which can be obtained through the use of a second harmonic manipulation: a theoretical 41% maximum increase is achievable in terms of output power, large-signal gain and drain efficiency over the Tuned Load design strategy, with a corresponding increase experienced for power-added efficiency. 75 D. Barataud, C. Arnaud, B. Thibaud, M. Campovecchio, J.M. Nebus, J.P. Villotte, ‘Measurements of timedomain voltage/current waveforms at RF and microwave frequencies based on the use of a vector network analyzer for the characterization of nonlinear devices – Application to high-efficiency power amplifiers and frequency-multipliers optimization’, IEEE Trans. Up-to-date pricing and reviews for solid state power amplifiers on the market can be found at the power amplifier reviews website.

4.6 Source/Load Pull Characterization Load pull techniques are adopted to test device output performance, not restricted to classical output power, large-signal gain, and efficiency. Figure 2.16 Optimum load RTL , DC power PDC,TL , output power PRF,TL for the tuned load operating condition, normalized to the corresponding Class A quantities and the drain efficiency ηTL devices have an almost constant gate-drain breakdown, and therefore biasing the device below pinch-off actually decreases the maximum drain-source voltage VBR,ds = VBR,gd − Vgs. The Doherty Power Amplifier 11.1 Introduction 11.2 Doherty’s Idea 11.2.1 Active Load Modulation 11.2.2 Impedance Inverting Network Implementation 11.3 The Classical Doherty Configuration 11.4 The ‘AB-C’ Doherty Amplifier Analysis 11.4.1 Fourier Representation for the Drain Current Waveforms 11.4.2 Behavioural Analysis 11.5 Power Splitter Sizing 11.6 Evaluation of the Gain in a Doherty Amplifier 11.7 Design Example 11.8 Advanced Solutions 11.8.1 Different Drain Bias Voltages 11.8.2 Doherty with Main Amplifier in Class F Configuration 11.8.3 Multi-way Doherty Amplifiers 11.8.4 Multi-stage Doherty Amplifiers 11.9 References.

Typically, RF power amplifiers drive the antenna of a transmitter Design goals often include gain , power output, bandwidth, power efficiency, linearity (low signal compression at rated output), input and output impedance matching, and heat dissipation. Figure 7.12 HF Class F amplifier design assuming a quadratic current waveform: (a) achievable drain efficiency; (b) normalized achievable output power level. Figure 7.11 HF Class F amplifier design assuming a sinusoidal current waveform: (a) achievable drain efficiency; (b) normalized achievable output power level.

CCA Φ Figure 7.3 Ideal performance for a Class F and reference TL amplifiers as functions of the CCA . Output power normalized to the Class A output at full swing. High Frequency Class F Power Amplifiers 7.1 Introduction The design of a PA is basically equivalent to the synthesis of a suitable circuit able to convert DC power supplied to an active device into RF/microwave power, subsequently transferred to an external load. The measured performance of the Class E amplifier in terms of output power, gain, drain efficiency and PAE is shown in Fig.

Finally, the Class E amplifier performance in terms of output power, gain, drain efficiency and PAE is reported in Fig. (5.40) has to be used in order to determine a step-by-step procedure, starting from the Tuned Load case (see chapter 2). In the following paragraphs the analysis of the voltage gain function δ and of the overshoot function β will be focused for different classes of amplifiers, while the design of power amplifiers based on harmonic tuning will be treated in greater detail in the following chapters 7 and 8. In low frequency applications, a large number of harmonic terminations (therefore well approximating the assumption of an infinite number of harmonics) can be effectively controlled: it is possible to achieve significant power efficiency levels, closer to the ideal figures, especially if the selected active device exhibits a very low knee voltage Vk and/or high breakdown voltage VBR The picture considerably modifies if the operating frequency range is moved towards the microwave region and beyond.

18, N. 4, April 2008, pp. 266-268 27 D. Barataud, F. Blache, A. Mallet, P.P. Bouysse, J.-M. Nebus, J.P. Villotte, J. Obregon, J. Verspecht, P. Auxemery, ‘Measurement and control of current/voltage waveforms of microwave transistors using a harmonic load-pull system for the optimum design of high efficiency power amplifiers’, IEEE Trans. The results are then usually represented reporting on a Smith chart the contour level curves for the selected parameter (i.e. constant output power, or efficiency, or IMD, etc.). Source/load pull measurements are widely used for the nonlinear characterization of a RF active device and consequently for the design of power amplifiers. HIGH EFFICIENCY SOLID STATE POWER AMPLIFIERS Table 2.3 Single-device PA performance under Tuned Load conditions for Class A and B bias and constant trasconductance.

HIGH EFFICIENCY SOLID STATE POWER AMPLIFIERS Table 2.1 Single-device PA performance with resistive loading for Class A and B bias and constant trasconductance. Time (psec) Figure 1.1 Example of active device output current and voltage waveforms for three different input power levels Pin Similarly, for the power gain the logarithmic scale is adopted, defining G dB = 10. log10 (G) = Pout,dBm − Pin,dBm. High Frequency Harmonic Tuned Power Amplifiers 8.1 Introduction 8.2 Theory of Harmonic Tuned PA Design 8.3 Input Device Nonlinear Phenomena: Theoretical Analysis 8.4 Input Device Nonlinear Phenomena: Experimental Results 8.5 Output Device Nonlinear Phenomena 8.6 Design of a Second HT Power Amplifier 8.7 Design of a Second and Third HT Power Amplifier 8.8 Example of 2nd HT GaN PA 8.9 Final Remarks 8.10 References.

FEATURES Circuitry designed by John Curl THX Ultra-certified Direct Coupled – no capacitors or inductors in signal path Input stage uses hand matched complementary JFETs 12 beta-matched 15 amp, 50 MHz bipolar output transistors 785VA Toroid power transformer with independent secondary windings for each channel, 40,000 µF power supply filter capacitance Independent power supplies for each channel DC Servo and relay protection circuits Highbias Class A/AB operation AC present, standby/normal, current overload indicators Tiffany-style RCA input jacks, loop output jacks 12 volt DC automatic turn-on circuitry Gold-plated 5 way speaker binding posts Custom designed removable IEC AC cord Rear mounted gain controls; ground lift switch 2 rack space height front panel Rack mounting adapter available SPECIFICATIONS Continuous Power Output – Stereo: 125 watts RMS x 2, 20 Hz – 20 kHz, 8 Ω, both channels driven; 200 watts RMS x 2, 20 Hz – 20 kHz, 4 Ω, both channels driven Continuous Power Output – Mono: 400 watts RMS, 20 Hz – 20 kHz, 8 Ω Current Capacity: 45 amperes peak per channel Slew Rate: >130 V/µsecond Power Bandwith: 5 Hz – 100 kHz, +0/-3 dB at 1 watt Total Harmonic Distortion: This activity resulted in the development of innovative design criteria for high efficiency and high linear power amplifiers, oriented to the optimization of power performance making use of harmonic tuning classes of operation. Spatium solutions are readily customizable and dramatically improve broadband RF power and efficiency through patented coaxial spatial combining techniques using gallium arsenide (GaAs) or gallium nitride (GaN) MMIC amplifiers Spatium’s all solid-state construction delivers longer service lifetimes than comparable TWTAs or conventional planar power combining products; they provide clear size, weight and power (SWaP) advantages.

Figure 7.30 Output current (a) and voltage (b) waveforms and resulting harmonic components, for the Class F amplifier. Figure 7.22 Output power and power-added efficiency vs. input drive level for a Class F (solid line) and TL (dotted line) in Class B. The TL case, when loaded by the same Class F fundamental frequency termination (dashed-dotted line), is also reported as a reference. Figure 7.18 Output power and power-added efficiency vs. input drive level for a Class F (solid line) and TL (dotted line) in Class AB The TL case, when loaded by the same Class F fundamental frequency load (dashed-dotted line), is also reported as a reference.

6.8 Class E Final Remarks The switched-mode and in particular the Class E approach gained large popularity for the design of high efficiency power amplifiers operating in the low RF spectrum. 6.7 Class E vs. Harmonic Tuned To compare the switched-mode (Class E) and the current-mode (harmonic tuned) high efficiency design approaches, a very pragmatic approach may consist in comparing the results achievable through a Class E design strategy, discussed in section 6.6.1, with the results that can be reached by using a different harmonic tuning strategy, and in particular a 2nd & 3rd HT amplifier, which will be fully described in chapter 8. Clearly this approach should be performed provided the same active device is used, preferably operated under the same conditions. Freq GHz Figure 6.33 S-band GaN Class E amplifier small signal performance: simulation (dotted lines) and measured (continuous line).

6.6 Examples of High Frequency Class E Amplifiers In the following several Class E amplifier designs are presented, in order to highlight the behaviour and the typical performance attainable when dealing with RF applications, making use of the previously discussed design strategy. The residual capacitance C x becomes mandatory to properly re-phase the fundamental component of the voltage across the switch and the current flowing towards the load resistance R. In fact, the parallel L − C P exhibits a residual inductive value, which has therefore to be compensated through the capacitance C x In this case, while the output voltage waveform across the active device appears to be quite similar to the classical Class E one, the resulting time-domain behaviour of the current waveform is substantially modified by the filtering action of the parallel resonating circuit L − C P , as reported in Fig. Two functions have been introduced, quite useful in the design procedure, i.e. the voltage gain function δ and the voltage overshoot function β. The former gives the percentage improvement achievable in terms of output power, large signal gain and conversion efficiency by means of a proper harmonic tuning scheme.

At the same time, the simultaneous maximization of output current and voltage swings within active device physical limitations actually guarantees maximum output power delivered to the fundamental frequency load. If Zn is identically zero (i.e. a short-circuit termination) for higher harmonics (n > 1), the Tuned Load case arises, already discussed in chapter 2. An overlap between output voltage and current waveforms does exist, and it has been demonstrated that the theoretical maximum efficiency (100%) is achieved only for a limiting deep Class C condition, i.e. for a current conduction angle (CCA) dropping to zero; such operation in turn however implies no power transferred to the external load, thus not representing a practical solution. Contributions in this field range from experimental observation of performance improvements 11-13, to the introduction of novel topologies as in the case of harmonic reaction amplifiers 14, 15, from systematic investigations of experimental performance 9 to design methods required for special harmonic tuning configurations 16. Together with harmonic tuning methods, somewhat alternative approaches are classified as ‘switching mode’ design schemes.

In this way, simultaneous maximum current and voltage waveforms swings are achieved, accounting for the device’s physical constraints 6. However, such a quasi-linear approach does not represent the best compromise, since potential beneficial effects of the harmonic load terminations are not exploited at all, while in actual cases they play a fundamental role to improve both efficiency and output power levels 7-10. Moreover, the highest power gain levels are ensured when biasing towards Class A conditions, in contrast with the highest efficiency values which are achieved biasing the active device in Class C. Consequently, appropriate design solutions are required, based on a suitable compromise on the achievable performance. 28 D. Barataud, M. Campovecchio, J.-M. Nebus, ‘Optimum design of very high-efficiency microwave power amplifiers based on time-domain harmonic load-pull measurements’, IEEE Trans.

26 C. Xian, J.D. Seok, P. Roblin, J. Strahler, R.G. Rojas-Teran, ‘High efficiency RF power amplifier designed with harmonic real-time active load-pull’, IEEE Microwave Wireless Components Lett., Vol. As discussed in chapter 2 in fact, referring to a simplified device model, it can be assumed, at least to a first approximation, that the output power (and the efficiency) performance is mainly related to the output loading condition (power match condition); the input termination becomes critical for the power gain (and power added efficiency) characterization. Figure 4.29 Example of load pull contour plots under large-signal conditions: (a) output power, in dBm, at 1 dB gain compression; (b) power-added efficiency, in percent, at 2 dB gain compression.

Under Class A bias, optimum intrinsic load condition, output power, DC power supplied and drain efficiency are estimated utilizing device physical limitations that impose an upper limit to current and voltage swings, thus obtaining RA = 2. Distributed amplifiers are outside of the scope of this book, and will not be treated; interested readers could refer to other textbooks on this topic 12. For moderate to large bandwidths, so-called corporate solutions are typically adopted, based on the full exploitation of the active device output I-V characteristics, and thus its nonlinear large signal operating conditions: proper power amplifier design strategies based on load-line concepts are implemented. As contrasted therefore to low-level (i.e. linear) amplifiers, often specified in term of small-signal gain, the absolute output power level, as well as the power gain, become the PA’s primary performance.

High Linearity in Efficient Power Amplifiers 9.1 Introduction 9.2 Systems Classification 9.3 Linearity Issue 9.4 Bias Point Influence on IMD 9.5 Harmonic Loading Effects on IMD 9.5.1 High Linearity and High Efficiency PA Design Process 9.5.2 High Linearity and High Efficiency PA Design Example 9.6 Appendix: Volterra Analysis Example 9.7 References. 7 High Frequency Class F Power Amplifiers 7.1 Introduction 7.2 Class F Description Based on Voltage Wave-shaping 7.3 High Frequency Class F Amplifiers 7.3.1 Effects of Device Output Resistance Rds. 6 Switched Amplifiers 6.1 Introduction 6.2 The Ideal Class E Amplifier 6.3 Class E Behavioural Analysis 6.4 Low Frequency Class E Amplifier Design 6.5 Class E Amplifier Design with 50% Duty-cycle 6.5.1 Practical Implementation and Variants of Class E Power Amplifiers 6.5.2 High Frequency Class E Amplifiers 6.6 Examples of High Frequency Class E Amplifiers 6.6.1 C-Band GaAs Class E Amplifier 6.6.2 X-Band GaAs Class E Amplifier 6.6.3 S-Band GaN Class E Amplifier 6.6.4 S-Band LDMOS Class E Amplifier 6.7 Class E vs. Harmonic Tuned 6.8 Class E Final Remarks 6.9 Appendix: Demonstration of Useful Relationships 6.10 References. Be sure to visit power amplifier reviews for the best solid state power amplifiers on the market to buy.

5 High Efficiency PA Design Theory 5.1 Introduction 5.2 Power Balance in a PA 5.3 Ideal Approaches 5.3.1 Tuned Load 5.3.2 Class F or Inverse Class F (Class F−1 ) 5.3.3 Class E or General Switched-mode 5.4 High Frequency Harmonic Tuning Approaches 5.4.1 Mathematical Statements 5.5 High Frequency Third Harmonic Tuned (Class F) 5.6 High Frequency Second Harmonic Tuned 5.7 High Frequency Second and Third Harmonic Tuned 5.8 Design by Harmonic Tuning 5.8.1 Truncated Sinusoidal Current Waveform 5.8.2 Quadratic Current Waveform 5.8.3 Rectangular Current Waveform 5.9 Final Remarks 5.10 References.

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