Analysis of a 10 to 300 MHz Amplifier with Transformer Feedback
Karl B. Niclas
and Michael Madera-Meza
Palo Alto, CA
Transformer feedback is used widely in amplifier design at UHF frequencies. The process' main advantage over resistive feedback is its nearly lossless characteristics, which produce significantly lower noise figures and, consequently, higher dynamic ranges without compromising other performance parameters. However, while amplifiers employing transformer feedback are broadband, their potential to conquer higher frequency bands is limited because the permeability of the ferrite core material decreases and core losses increase rapidly with frequency. In addition, capacitive parasitics exert a growing influence with frequency and ultimately limit the performance.
Four-port directional couplers by means of ferrite transformers are the dominant feedback elements used in so-called lossless feedback amplifiers. This type of amplifier was first proposed by David Norton and patented in 1971.1 Norton's innovation was preceded by K. Simmons' invention of the directional coupler in 1962,2 and C.G. Sontheimer's patent of a broadband directional coupler in 1969.3 Many more important developments have emerged in subsequent years using parallel as well as series feedback with transformers.4,5.
Above 10 MHz the frequency dependence of the core material and the parasitics of the feedback element become major factors in the performance of an amplifier employing transformer feedback. These factors make a quantitative analysis of the feedback process rather difficult. To perform an accurate analysis that takes these factors into account, the performance of a 10 to 300 MHz amplifier based on the measured four-port scattering parameters (S-parameters) of its feedback element will be analyzed. Basically, the design follows the concept of Norton's high dynamic range amplifier.1 However, it makes use of six transformer coils rather than the four discussed in Norton's patent. This modification, which is used commonly in the industry, adds an additional degree of flexibility to the device tunability.
Figure 1 shows a schematic of the amplifier. The unit's main elements are the bipolar transistor Q1 and the feedback transformer assembly consisting of two transformers (T1 and T2) wound on separate ring cores. The DC-biasing circuitry comprises the resistors R1 through R3, the bypass capacitors C2 through C4 and the blocking capacitors C1 and C5. The resulting operating conditions chosen for the amplifier were VBE = 0.86 V, IB = 0.51 mA, VCE = 10.9 V and IC = 85 mA.
The Feedback-transformer Assembly
The main purposes of feedback circuits for amplifiers are to provide good gain flatness and to improve the input and output return loss. These objectives can be accomplished easily with resistive feedback. However, the noise generated by the feedback resistor increases the noise figure.6 To minimize this degradation, a lossless feedback circuit is required that can be provided by transformer feedback. While resistive feedback has virtually no frequency limit as long as the active device supplies sufficient gain, the transformer's core permeability and winding capacitive parasitics create an upper frequency limit somewhere below 1 GHz. A schematic of the four-port transformer is shown in Figure 2 . Since the losses and permeability of the core material vary significantly with frequency, the transformer was characterized by measuring its S-parameter across the 10 to 300 MHz frequency band. As is customary, all source impedances and port terminations were Zo = 50 W. There are 16 S-parameters to a four-port unit, that is, the reflection coefficients at each port Smm and the transmission coefficients Smn for m p n (m = 1,...,4; n = 1,..., 4). However, the four-port transformer is a reciprocal network, Smn = Snm, which produces six transmission coefficients and four reflection coefficients Smm that characterize the feedback transformer completely. The six transmission coefficients and the four reflection coefficients are plotted on Smith charts in Figure 3 . Because the transmission parameters represent the voltage gain between two ports, Vm/V50 = Smn in this 50 W system where V50 is the voltage that a 50 W source delivers to a 50 W termination. Therefore, several conclusions can be drawn from the measurements taken between 10 and 300 MHz.
At least 80 percent of the voltage at port 1 (input port) arrives at port 3 (base port) at a maximum phase shift of 24°. A similar situation exists for the voltage at port 2 (collector port) of which more than 72 percent appears at port 4 (output port) at a maximum phase shift of 33°. The magnitude of the voltage at port 3 (base port) transmitted or fed back from port 2 (collector port) is between 11 and 8.5 percent of the port 2 voltage with insignificant change in phase. A negligible amount of port 2 voltage (collector port) is transmitted to port 1 (input port). The same is true for the voltage of port 4 (output port) transmitted to port 3 (base port). Moderate coupling was measured between ports 1 and 4.
While the characterization of the transformer assembly is a necessary tool to compute the performance parameters of the amplifier, it is virtually impossible to quantitatively predict the behavior of the amplifier based only on the knowledge of the feedback transformer's 16 S-parameters due to the transistor's complex input and output impedances, which obviously are significantly different from Zo = 50 W. However, it is important to understand the characteristics of the transformer circuit as a stand-alone unit in a standardized environment (50 W system) for future improvements and new designs and, ultimately, to optimize the feedback transformer's performance.
A computer analysis of the amplifier using the measured four-port parameters of the feedback transformer circuit was performed. Since the active device is a bipolar transistor, that is, a current-controlled current source, the analysis was limited to the RF currents. The computed currents at the base port IBAS, collector port ICOL and output port IOUT normalized to the input current IINP are shown in Figure 4 . The current IBAS enters the base port of the bipolar transistor in the direction indicated and at a phase shift between 14° and 69° with respect to IINP. Most importantly, the current ratio IBAS/IINP increases with frequency, providing a nearly constant gain across the frequency b and. At f = 300 MHz, the amplitude of IBAS exceeds that of IINP by 0.92 dB, that is, the initial negative feedback has changed to slightly positive feedback. The amplitude of the current ratio IOUT/IINP reaches a maximum of 9.2 dB at 100 MHz and decreases to 7.2 dB at 300 MHz. Note that since all currents IXXX are normalized to the input current IINP, the ratio 20log?IOUT/IINP? is not identical although it is proportional to the power insertion gain. This result is due to the fact that the input impedance of the amplifier ZINP is not equal to Zo. The power insertion gain is SSG = 20log?IOUT/I50?. The input current IINP normalized to the current I50, which is the current when a 50 W source is terminated by a 50 W load, is also plotted as IINP/I50. While the phase angle between IINP and I50 is relatively small, the magnitude ratio is significant.
The computed small-signal gain (SSG), input return loss RLINP and output loss RLOUT are shown in Figure 5 . The curves demonstrate clearly the effect of the transformer feedback on gain flatness as well as the amplifier's input and output return loss across the 10 to 300 MHz frequency band. However, the most important feature of the transformer feedback amplifier for this band is its low noise figure when compared to resistive feedback amplifiers of equivalent output powers.
Measured Amplifier Performance
The feedback amplifier's measured SSG and return losses (RLINP and RLOUT) are shown in Figure 6 . Across the 10 to 300 MHz frequency range, a gain of SSG = 16.6 ±0.45 dB at return losses RLINP < –11 dB and RLOUT < –17 dB were recorded. A comparison between the measured and computed performance parameters shows good agreement for the gain and input return loss and acceptable agreement for the output return loss. While instability was a concern, none was measured when terminating the amplifier with a sliding short or computed using the amplifier's measured S-parameters. The measured noise figures and output powers at the 1 dB compression point (P1dB) are shown in Figure 7 . Third-order intercept points (IP3) ranged from IP3 = 40.7 to 43.2 dBm between 10 and 200 MHz, and decreased to 38.5 dBm at 250 MHz.
A detailed analysis has been performed of a feedback amplifier using a transformer feedback loop. The analysis was based on the measured four-port S-parameters of the feedback transformer circuit. The currents of the amplifier assembly were studied, explaining the feedback mechanism at work in these types of amplifiers when all transformer parasitics are taken into account. Good agreement was achieved between the computed and measured performance parameters of the amplifier.
1. D. Norton, "High Dynamic Range Amplifier," US Patent 3,624,536, November 1971.
2. K. Simmons, "Directional Coupler," US Patent 3,046,798, August 1961.
3. C.G. Sontheimer, "Broadband Directional Coupler," US Patent 3,426,298, February 1969.
4. G. Vendelin, A. Pavio and U. Rhode, Microwave Circuit Design Using Linear and Nonlinear Techniques, Wiley Interscience, 1990, pp. 242–250.
5. M. Martin, "Ferrite Transformers Minimize Losses in RF Amplifiers," Microwaves & RF, May 1990, pp. 117–126.
6. K.B. Niclas, "Noise in Broadband GaAs MESFET Amplifiers with Parallel Feedback," IEEE Transactions Microwave Theory and Techniques, Vol. MTT-30, January 1982, pp. 63–70.
Karl B. Niclas received his Dipl Ing and doctorate in engineering from the Technical University of Northrhine-Westfalia, Aachen, Germany, in 1956 and 1962, respectively. He has worked at the General Electric Microwave Laboratory, Palo Alto, CA, and Telefunken, Ulm/Donau, Germany. Currently, Niclas is a principal scientist at Watkins-Johnson Co., Palo Alto, CA. He is a recipient of the 1962 Outstanding Publications Award of the NTG (German Society of Radio Engineers) and the 1985 MTT Microwave Prize.
Michael Madera-Meza is presently the thin-film components test foreman at Watkins-Johnson Co., Palo Alto, CA. He supervises and is responsible for the testing of TO-8 and cascadable amplifiers, as well as VCO and thin-film components. Prior to this activity, he helped to develop a variety of TO-8 and cascadable amplifiers, and worked for four years on wideband amplifiers within the 500 MHz to 18 GHz frequency range.