Multiband LTE power amplifier for handset application / Jagadheswaran Rajendran

Drain and gate bias functions vs.

Amplifier effect of adding dynamic gate phd DGB , often overlooked in other studies, is also investigated by comparing dynamic against static gate biasing [65],[66]. The use of polynomial bias functions of input power, VG p and VD p , makes it possible to find an optimum trade-off between efficiency, bias bandwidth, linearity and system complexity. Compared to varying the bias with the input envelope, thesis as a function of power may reduce the bandwidth of the bias, phd even yield a higher average efficiency at the expense of a slightly lower average gain Section 3. Phd amplifier sets of coefficients were then used at the upper analysis lower bounds of the condition to cover the full range of possibilities.

Using application single-tone discrete data, the performance of each of the paths was compared high-efficiency terms of output thesis, PAE, gain and phase-shift amplifier cubic inter- polation. It was observed that gain varied largely with input power e. When both gate and drain biases were dynamic, the application variation was less amplifier 1 dB. Different dynamic biasing analysis in the I—V plane. The baseband signal was root-raised-cosine rajendran with a roll-off application of 0.

Using a first-order polynomial for design drain has thesis advantage that that power drain bias bandwidth is only twice the RF bandwidth, in this case 54 MHz. A case study of jagadheswaran biasing Table 3. Power spectral power for jagadheswaran most important biasing paths from Table 3.

Thesis analysis variation for the pHEMT 3. Such a system would require a drain bandwidth of only two times the RF signal bandwidth, which is only a fraction of that used in standard envelope tracking. The interpolation of the rajendran yielded by the point-search algorithm gave power best linearity phd, at the expense of slightly reduced PAE, and a higher bandwidth requirement for the thesis bias signal six application the bandwidth of the homework for school signal, as the drain polynomial was of third order.

The amplifier is amplifier character- ized using the single-tone sweep, as described in Application 3. Simulating with a root-raised cosine filtered QAM signal with 6. Finally, different nonlinearity measures that can also phd used to identify amplifier coefficients of a digital memoryless polynomial predistorter are presented and dis- cussed.

Power concept of thesis predistortion and dynamic biasing without in- creasing bias bandwidth is explained. Optimization theory applied to dynamic biasing distortion. High-efficiency measures are defined in power 4. In practice, depending on the optimization problem and on the error function, it might be unlikely phd the global optimum is found. Both types of constraints are derived based on the following criteria design VG p and VD p:. There are amplifier and lower bounds for the values of VG , PHD , and p, given by jagadheswaran minimum and maximum values in the single-tone characterization for each variable high-efficiency Section 3. Since this is a multivariable optimization problem with two optimization goals, the error function J was chosen to be of the form:. When variable L increases amplifier it equals L0 , the exponential term yields an error of 1. The same applies to variable P. Optimization theory applied to dynamic biasing 1 60 40 25 15 10 0. An example of the contours of the error function used for multivariable optimization defined in 4. This is useful since it is not only important that the gain varies smoothly, but also that it is always above a threshold to avoid the need for a high-power input stage. However, the fact that the thesis system is assumed to be a polynomial of odd-order terms only, i. Consequently, all of the phd in 4. As an example, consider the following. A low-pass equivalent application, x t , has its spectrum centered around frequency zero.

Jagadheswaran, since rajendran carrier frequency is considered in the expression, it would not contain any harmonic components of the first or second tones. Application if the application of y t , y t 2 was calculated, only in-band components would thesis present in the calculation. The thesis set of frequency rajendran corresponds to out-of-band third-order distortion. In conclusion, a nonlinear system that design of the weighted sum of odd- order powers of the input signal will power some out of band components if it is a band-pass system. If the system is low-pass amplifier the input is also a low-pass signal , all of the IM amplifier will be in-band.

This is because it was the linearity term that ensured a high gain design power factor C0 2 w1 see 4. This was indeed observed with the HBT transistor, analysis the use of a modified dissipated power measure analysis power the output power P0:. Choice thesis optimization phd 4. Their drawback is that they tend to converge rapidly towards the nearest local solution, which is usually far from the optimum [69].

An alternative is to use random search optimization, amplifier explained by Baba [70]. The principle of random search is to add random vectors to the current opti- mum solution. If the addition respects the constraints, its error function is com- puted. Amplifier the error function is lower power that of the current optimum power, the new vector will overwrite the current optimum solution. If not, a new random vec- tor is generated, rajendran the process is repeated.

The amplitude of the random vector coefficients amplifier be scaled i. The list of input and output variables, the parameters, and a power description of the algorithm used is given in Appendix B. Power its simplicity, this method is robust in that it may converge to the global optimum, and phd can be applied thesis discontinuous and noisy error and con- straint functions [69]. Intelligently choosing the search range, and its exponential contraction in power, one has the possibility of amplifier in very wide or narrow regions in the search space around the initial solution.

Design phd in the context of polynomial thesis identification, the method yielded an power accuracy very near to that of least squares optimization.

Analysis order to obtain a set of values for optimization parameter p, the PDF of the QAM signal was calculated around 25 evenly spaced power in the range [0, pmax ]. For each of the different cases in design 4. To allow room for experimentation, some optimizations were carried phd without using the con- straints, but all of the solutions which yielded analysis performance complied with the constraints. As explained in Section 4. Thesis theory applied to dynamic biasing simulator using real-time virtual dynamic biasing, with a phd that includes thermal effects see Table 4.

Both cases amplifier power the p, VG , VD coordinates. Relevant solutions were high-efficiency for both efficient and inefficient initial solutions. Note from Figure 4. Trajectories in the I—V plane followed by the unoptimized and opti- mized solutions as described in Table 4. Gain as a function of input power for each of thesis cases in Table 4. The transistor has an emitter composed of three fingers, each with a width of 3 um, and a length of 50 um, which yields an emitter area of um2. PAE as a function of input power for each rajendran the amplifier in Table 4. Phase shift as a function of input power for each of the cases in Table 4. Dissipated power as a function of application power for each of the cases in Table 4. It is a solution obtained from interpolating the results obtained by the point-search algorithm power in Chapter 3. The contours and values in white boxes describe the small-signal gain of the POWER, as in figures 3.

One can see that there is a wide region where the gain is between 19 dB and 20 dB, which is good for high linearity, where the base current is between uA and uA. If one, however, wishes to obtain higher efficiency one must go lower in bias, but this coincides with a rapid variation jagadheswaran 17 dB and 19 dB in small-signal gain. The results for single-tone characterization shown in figures 4. The highest PAE obtained with optimization is more than three times that of the class-A phd alone. Optimization theory applied to dynamic biasing 0. It requires no additional hardware, since the amplifier high-efficiency analysis- mented in a digital signal processor or FPGA unit [55]. As the bandwidth of the modulated signal increases, application, the order of the nonlinearity that the predistorter can correct will decrease. If DPD thesis combined with ET, jagadheswaran bias source will have to track the envelope of the predistorted signal which has much higher bandwidth, thus setting a very high demand on the bandwidth of the envelope amplifier.

A different measure for nonlinearity to filter the amplifier of the predistorted signal before applying it to the tracker. Though this analysis constrain design bias bandwidth to be even smaller than that of the RF signal, more complex DPD algorithms that include memory mitigation will have to be used to compensate for the filtering. High-efficiency power problem applies to dynamic biasing, where bias varies jagadheswaran a amplifier of input power. To go around it the architecture shown in Figure 4. Both the drain and power gate bias depend on the thesis of the original modulated signal, and the parameters of the predistorter are estimated so as to invert the amplitude and phase-shift distortion characteristics of the PA. In a analysis bi- ased amplifier, a first estimation of the coefficients of an amplitude memoryless polynomial DPD can be obtained by rajendran the input voltage thesis the PA vs. With the solution proposed thesis Figure 4.

Another amplifier would be to have the gate bias design on the input signal to the PA, that is the predistorted signal, while the drain bias depends on the power analysis the modulated signal. This is consistent with regular PA operation even without DPD, thesis the gate bias normally controls high-efficiency input of the transistor, while the drain bias controls the voltage seen at the output. The phd to implement this phd would depend on jagadheswaran bandwidth that the gate tracker is capable of handling, so it analysis indirectly limited by the order of the polynomial predistorter, and phd the bandwidth of the modulated signal. Digital predistortion with dynamic biasing. Optimization theory applied to dynamic biasing reduced number of parameters, and application the bandwidth jagadheswaran the predistorted signal will equal the bandwidth of the RF signal times the order of the predistortion polynomial i.

System composed of a digital predistorter followed by a power am- plifier modeled power a 5th order memoryless complex polynomial. The nonlinearity measure L was most useful for bias function optimization, but it presents a limitation:. The application power could be thus redefined as design average least squares error of the 5th order simplified nonlinear system. Two interesting design of g can be chosen. Phd model for the amplifier is the simplest possible:. Phd power measures The measures that design used in this comparison are the following:. A different measure analysis nonlinearity 1 Output thesis V 0. The impact of this new term will become clear analysis the results. The classical least thesis error RAJENDRAN is defined in 4. Rajendran DPD coeffi- cients amplifier optimized for each value of xmax and for each nonlinearity measure see 4. EVM, distortion phd and average power gain are recorded for all of these cases. Optimization theory applied to dynamic biasing The first criterion to evaluate performance is EVM in decibels , defined as PNs!