Class E F Amplifiers Normalized Output Power EECS 242 It s easy to show that for Class A B C amplifiers the efficiency and output power are given by It s useful to normalize the output power versus the product of Vbk and Imax Idc Prof Ali M Niknejad C 2009 Class A B C EECS 242 As efficiency improves the normalized output power drops from 10 down to 0 Prof Ali M Niknejad C 2009 Class A B C Properties EECS 242 Keep voltage waveform sinusoidal amplitude is limited to Vdd 2 Only way to improve efficiency is to control current Require very large on current to deliver power Prof Ali M Niknejad C 2009 Class F Start with Class B current waveform only odd harmonics Tune impedance at odd harmonics to be an open circuit to dissipate no harmonic power but allow odd harmonics in voltage waveform Tune even harmonics to short circuit to avoid dissipating power EECS 242 Prof Ali M Niknejad C 2009 Class F Waveforms EECS 242 Maximally flat Class F waveforms An ideal Class F amplifier has a square voltage waveform and 100 efficiency Prof Ali M Niknejad C 2009 Class F Efficiency In theory if you can control an infinite number of harmonics efficiency approaches 100 EECS 242 Prof Ali M Niknejad C 2009 Class F Output Power Square wave has a peak fundamental 4 larger than the peak 1 dB output power enhancement EECS 242 Prof Ali M Niknejad C 2009 Class F Disadvantages EECS 242 Output capacitance of device not naturally absorbed into network need inductor to tune it out Difficult to control more than 5th harmonic resonators are lossy and additional losses present diminishing returns on efficiency Prof Ali M Niknejad C 2009 Switching Amplifiers EECS 242 Operate transistor in triode region where it acts like a switch For an ideal switch the power dissipated in the switch is zero right Are all switching PA s the same Prof Ali M Niknejad C 2009 Linear Time Varying Systems Even though transistor is non linear the operation of the periodic switching action can be modeled as a linear time varying periodic system The design of the output network completely determines the behavior of the circuit EECS 242 Prof Ali M Niknejad C 2009 ce is on the voltage waveform for part of the cycle and on the current 42 the switch is closed the switch voltage Chapter he remainder Specifically when vs 3 Switching Amplifier Properties I V Solution for Swithing Amps o but when open the current is is forced to zero If the set of times during ch is conducting is denoted D and the set of non conducting times denoted onditions can be written as D vs 0 3 4 D is 0 3 5 these two constraints the switch makes no demands on the waveforms the constrained portions ofFigure the waveform are amplifier trivial to generate the 3 2 Switching waveforms after applying switching constraints Non zero values of current and voltage are not yet determined For trans conductance non zero portions require additional effort amplifiers the current is known so the voltageconstraint is determined theharmonics load network imposed onlyby at the Letting Zin k denote the impedance at the kth ely obvious that the form of the non zero portions of the waveform must be harmonic In a switching amplifier when the switch is on the voltage mehow by the properties of the load network The load network is LTI and is forced to zero and the current through the switch can j and the ibed completely by its frequency dependent input impedance k kso v i e Zin kis off the take on any value Likewise when the switch k k 3 6 influence it could have on the waveforms is to demanding that at all switch current is zero but the voltage take on any k 1 2can 3 4 he ratio between the voltage and current on its port be equal its port value Although this condition is easily written down it is still not obvious how to apply it in nce the waveforms only contain order toharmonic determine frequencies the waveforms this Thebecomes difficulty alies in the fact that 3 6 is really an EECS 242 Prof Ali M Niknejad C 2009 infinite number of independent frequency domain conditions which must be reconciled with the very tight time domain conditions demanded by the switch Considerable effort ntal period T Similarly the waveforms will be assumed to be periodic having the damental period Figure 3 2 Switching amplifier waveforms after applying switching const Non zero values of current and voltage are not yet determine Impedance at Harmonics ilizing this assumption the switch voltage and current waveforms vs and is ely may be expressed in terms ofconstraint a Fourier series imposed only at the harmonics Letting Zin k denote the impeda harmonic v s V DC v k cos k k v k ik e k 1 is I DC i k cos k k k 1 3 1 j k k Zin k k 1 2 3 4 3 2 Although this condition is easily written down it is still not obvious how determine the where waveforms The difficulty lies in the fact that 3 6 ik the normalized values of the parameters VDC Iorder DC vk to k and k and able is defined as infinite shape number therefore of independent frequency domain conditions which must The waveform is completely determined with the t very impedance tight time domain conditions demanded by the switch Cons by the load network it s a linear system 2 f t 2 3 3 0 T viewed from this perspective has been exerted to solve for these waveforms even for specific cases such Waveform Constraints of class E solutions 4 31 42 each solving for a slightly different circuit top approximations and assumptions determination the voltages and different currents for the a switching amplifier can be Typically the solutions are deriv domain using network utilizing to determining the voltages and currents on the switch theory itself Once these different simplifying assumpti EECS 242 Prof Ali M Niknejad C 2009 ms are known the other circuit waveforms follow readily using standard linear topology making generalization or comparison difficult To date there has b a dual or inverse switching amplifier tuning This can be done by simply inv drive of the switch so that the switch will be on at times where before it was Inverseadmittance Class of numerically equalOperation to the original load network s impedance To see vise versa and by using a tuning network presenting at each harmonic clearly consider 3 1 3 6 rewritten as follows EECS 242 By duality any PA can be transformed into it s dual where the role of current voltage are switched by imposing the complementary admittance condition For instance a Class D voltage switching amplifier can be transformed into a current switching