Radio Frequency Power Amplifiers

Using the high frequency voltages \(V(t)\) and currents \(I(t)\) in time domain is a suitable approach for describing the behavior of non-linear radio frequency (RF) circuits. Fig. 17 shows the schematic of the measurement setup based on a sampling oscilloscope and a directional coupler. The measurement setup is realized as a microstrip technology circuit with a reference plane set to a position on a microstrip line with a characteristic impedance of \(Z_0\) = 50 Ω. The directional coupler separates the incident and scattered waves of the DUT. The coupled voltages \(V_{3}(t)\) and \(V_{4}(t)\) are measured in time domain with the sampling oscilloscope.

To calculate \(V(t)\) and \(I(t)\) in the reference plane the measurement setup has to be calibrated taking into account the frequency response of the measurement setup (including the directional coupler and cables). In this context, a TOSM (Thru, Open, Short, Match) calibration procedure is enhanced by using calibration standards pre-characterized via the TRL (Thru, Reflect, Line) method. Therefore, the frequency of the RF source is swept to the distinct frequency points, i.e. to the fundamental frequency \(f_1\) and to the considered higher harmonics (up to 6\(f_1\)). The four-port coupler can be defined by means of the four-port / two-port reduction and thus can be described by a 2x2 error matrix E with coefficients \(e_{xy}\) for each frequency point, which are shown in Fig. 18.

To determine the accuracy of the in situ measurement approach a comparison between a direct measurement and the in situ measurement with the coupler is conducted. For the measurements the sampling oscilloscope Agilent 86100B with module 86117B is used. As signal source the signal generator Agilent 4430C is utilized and synchronized to the oscilloscope. At first, the in situ determined impedance of a passive load in the reference plane is compared with a VNA (Rohde & Schwarz ZVA24) measurement. Furthermore, waveform is verified through direct measurements in comparison to the in situ measurement approach. 

As a reference the impedance in the calibration plane is directly measured with a TRL calibrated VNA and obtained from the in situ measurement approach with the directional coupler. The test board is identical to the one of the calibration setup. Therefore, a verification reflection termination \({{\Gamma }_{\text{verify}}}\) is connected to the coupler, which translates to the measured \({{\tilde{\Gamma }}_{\text{verify}}}\) in the reference plane and its impedance \({{Z}_{{{{\tilde{\Gamma }}}_{\text{verify}}}}}\). The results for the normalized impedance \({{Z}_{{{{\tilde{\Gamma }}}_{\text{verify}}}}}/{{Z}_{0}}\) are presented in Fig. 19. The comparison between both methods in a frequency range of 0.5 GHz to 6 GHz shows a good agreement.     

Furthermore, in order to exhibit the accuracy of the waveform measurement a test circuit is used, which consists of two diodes, one connected in series to a microstrip line and the other one connected to ground. At the left hand side of the circuit a directional coupler is embedded, which is an exact reproduction of the one on the calibration board. The RF source provides an available source power of \(P_{in}\) = 6 dBm with a frequency of \(f_1\) = 1 GHz. The resulting voltages \(V(t)\) in the reference plane are calculated in MATLAB for the in situ measurement approach as well as for a direct measurement with the sampling oscilloscope directly connected to the test circuit. A comparison of the results in Fig. 20 shows a good agreement of both measurements. The diodes clip and attenuate the input signal. As a result of the non-linear behavior of the diodes the signal contains higher harmonics. Thus, Fig. 20 indicates the functionality of the in situ waveform measurement system for the fundamental frequency and the higher harmonics.    

The interaction of the carrier and the peak amplifier can be described by the fundamental high frequency voltages and currents. Hence, Fig. 21 shows the relationship of the magnitude of the high frequency voltages (\(\left| {{V}_{C}}\left( {{f}_{1}} \right) \right|,\left| {{V}_{P}}\left( {{f}_{1}} \right) \right|)\) and currents \(\left| {{I}_{C}}\left( {{f}_{1}} \right) \right|,\left| {{I}_{P}}\left( {{f}_{1}} \right) \right|)\)) at \(f_1\) in the reference plane of the carrier and the peak amplifier over the normalized output power \(P_{out}=P_{out,max}\). In the high power range both amplifiers are active and the current of the carrier amplifier increases, while the voltage is approximately constant, which results in the high efficiency in this range. In general, a satisfying agreement between simulation and measurement exists. However, there is still some potential for improving the load modulation with help of the in situ measurements in a proceeding development process.