2.2. Electrical memory effects
This Section first presents the impedance definitions of transistor amplifiers. The distortion composition is then analysed in more detail and compared with the single polynomial model, and finally the effects of matching impedances in terms of memory effects are discussed.
The notations for CE BJT and CS MESFET amplifiers given in Figure 2-4 are used throughout this thesis. ZB(match) is the driving impedance of the stage, from which the base bias impedance ZB(bias) is excluded. These two correspond to the impedance measurable by a network analyser (NWA) upon disconnecting the transistor. ZB(int) is an internal base impedance which is bias-dependent. Similarly, the external collector impedance consist of a load impedance ZL and a collector bias impedance ZC(bias), and both measurable from a collector node. Correspondingly, ZC(int) is an internal collector impedance. Node impedance means the impedance level of the node, however, and the impedance of base and collector nodes can be calculated by
and
Similarly, by changing the names of the terminals, equations can be found for the node impedances of the MESFET presented in Figure 2-4b. A name input impedance is used in both BJT and MESFET instead of a source impedance in order to avoid misunderstanding in the source terminal of the MESFET. In addition, Equations (9)-(10) describe the node impedance outside the transistor, although the impedance seen by the internal distortion generator is the primary object of interest. The internal base series resistor and emitter impedance are excluded in this way, but they will be taken into account in simulations and analyses to be presented in later Chapters.
Real power amplifier devices have more than one nonlinearity mechanism, and these interact, which means that the nonlinear responses are not just the output signals as assumed in (4), but cause new nonlinear responses. Thus, to gain an insight into distortion mechanisms, the transistor amplifier will be considered a cascade of two polynomials in the following presentation. This model still lacks any feedback effects as compared with a real amplifier, but it is otherwise informative and provides an insight into distortion composition.
Figure 2-5. Representation of the cascade connection with Volterra operators of orders one to three.
A cascade of two connected polynomials can be presented in the form of the block diagram given in Figure 2-5 (Wambacq & Sansen 1998). Block H describes the base voltage as a function of the input signal, and block F the collector voltage as a function of the base voltage. H1, H2 and H3 correspond to the different order nonlinearities represented by the coefficients a1, a2 and a3 in (4). The generation of IM3 by means of 3rd order terms is straightforward (Maas 1995). First, the 3rd order block H3 of the base nonlinearity causes an IM3 signal at the base, which is amplified in F1, and second, a linear signal at the base goes to the 3rd order nonlinearity of the transconductance F3, causing IM3. Generation of IM3 by cascaded 2nd order mechanisms is a little more complicated. First, the envelope component at the base is generated in H2, which creates the IM3 component with a linear signal at the base H1 in the 2nd order nonlinearity of the transconductance F2. Similarly, mixing from the 2nd harmonic causes IM3, as seen in Figure 2-5.
A frequency domain combination of nonlinearities of different orders is given in Figure 2-6. Figure 2-6a presents the output of the first block (4), and the amplitude of the IM3 component can be calculated from (7). This multi-tone signal is the input signal for the second block, and the output IM3 now combines with other frequency components. The envelope signal ω 2-ω 1 and the upper two-tone signal ω 2, for example, will be mixed in the 2nd order nonlinearity of the latter block, which results in the generation of an IM3 signal. Similarly, the 2nd harmonic of the upper input signal 2ω 2 and the lower input signal from the negative frequency side -ω 1 will produce an IM3 signal. As a result, IM3 sidebands are affected not only by fundamental voltage waveforms, but also the voltage waveforms of the different nodes at the frequency of the envelope ω 2-ω 1 and 2nd harmonics 2ω 1 will have an impact on IM3.
Figure 2-6. a) Spectral components produced by nonlinearities up to the 3rd order and b) composition of IM3.
The question is how to control the voltage waveforms of the different nodes and frequency components. Since the nonlinearities of the circuit components can be regarded as current sources, as will be explained in Chapter 3 (Wambacq & Sansen 1998), their voltage waveforms can be affected by node impedances. The composition of IM3 in the real power amplifier device is sketched in Figure 2-6b, with nonlinearities up to the 3rd order (Sevic et al. 1998). The greatest part of the distortion is produced by 3rd order distortion mechanisms, which are affected by fundamental impedances, but 2nd order mechanisms generated by the envelope and 2nd harmonic frequencies also have a significant effect on IM3 distortion, and can be controlled by node impedances at these out-of-band frequencies.
Electrical memory effects are caused by varying envelope, fundamental or 2nd harmonic node impedances at different modulation frequencies. Measured gate node impedances for a MESFET amplifier in the dc, fundamental and 2nd harmonic bands are given in Figure 2-7. Centre and maximum modulation frequencies are 1.8 GHz and 20 MHz, which means that the dc band is important up to 20 MHz and the fundamental band between 1.77 GHz and 1.83 GHz, because the whole IM3 band of 60 MHz is interesting in terms of IM3 distortion. The important 2nd harmonic band is between 3.58 and 3.62 GHz. The fundamental impedance can easily be kept constant over the entire modulation frequency range, because it is 0.3% from the centre frequency in that example. Also, the range of the 2nd harmonic impedance is quite narrow, and matching is simple if traps for attenuating harmonic responses are avoided. Such traps cause huge impedance variations and are a significant source of memory effects. As fundamental and second harmonic impedances play a minor role, the major part of the memory effects is produced by envelope impedances. Envelope frequency varies from DC to 20 MHz, and the gate node impedance, for example, must be constant or very low over this region in order to avoid memory effects. This is not the case in the practical implementation presented in Figure 2-7, however, where the gate impedance at the envelope frequency varies by approximately 2 decades. It can be concluded that, with careful design, the memory effects introduced by various terminal impedances can be limited to that converted from the envelope frequency. A thorough analysis of distortion mechanisms is presented in Chapter 3, where the distortion mechanisms and memory effects of the BJT and MESFET amplifiers are analysed in detail.