Negative Input Resistance and Real-time Active Load-pull Measurements of a 2.5GHz Oscillator Using a LSNA

Transcription

1 Negative Input Resistance and Real-time Active Load-pull Measurements of a.5ghz Oscillator Using a LSNA Inwon Suh*, Seok Joo Doo*, Patrick Roblin* #, Xian Cui*, Young Gi Kim*, Jeffrey Strahler +, Marc Vanden Bossche, Roberto Rojas*, and Hyo Dal Park* *The Ohio State University, + Andrew Corporation, NMDG Engineering, # roblin@ece.osu.edu Abstract A large-signal measurement-based methodology to design oscillators using the Kurokawa theory is presented in this paper. Measurements of the negative input resistance and device line of a.5ghz HEMT oscillator versus frequency and power, and its optimization using real-time active load-pull (RTALP) for the nd and 3 rd harmonics are performed with a large signal network analyzer (LSNA). As a result, the maximum output power of the oscillator is increased from 3.mW to 38.8mW. Finally self-oscillation is verified using a load tuner to yield an output power and frequency of oscillation in reasonable agreement with the Kurokawa analysis. Index Terms Real-time Active load-pull, large signal network analyzer (LSNA), negative input resistance, oscillators O I. TRODUCTION scillators are essential components of radio frequency (RF) transceivers in wireless communication systems. Typically RF oscillators are used together with mixers for frequency translation []. In order to design an optimal oscillator, it would be greatly beneficial to be able to measure its device line (non-linear device impedance versus oscillation amplitude). The later ones can be used in turn to optimize the output power and the phase noise characteristics of the oscillator [], [3]. By finding the optimal embedding network of the oscillator at the fundamental frequency, the output power can be maximized [4], [5]. However, a poor selection of harmonic load impedances could degrade the performance of the oscillator. A study of the effect of the second harmonic load impedance as well as the device line characterization has been reported using active load-pull measurements [6]. The reported measurements indicate the importance of the harmonic load impedances in optimizing the oscillator s output power and efficiency. In this work we present a real-time active load-pull system which greatly reduces the acquisition time and facilitates the sweeping of the harmonic phases while recording the RF and DC characteristics at each phase setting. This work was supported in parts by a National Science Foundation grant. The multi-harmonic real-time active load-pull technique introduced by [7] using an LSNA is applied here to the characterization of the.5ghz oscillator. The LSNA remarkably simplifies the entire measurement process. The test oscillator circuit and the LSNA test bed are presented in section II. Measurement results obtained for the oscillator with this test bed are reported in section III. Finally a self oscillating circuit implemented with a load tuner is demonstrated in section IV and a summary of this work s achievement is given in section V. II. MEASUREMENT SET-UP DESCRIPTION A. Oscillator Design The oscillator realized with an ATF5443 HEMT from Agilent is shown in Fig.. The HEMT oscillator circuit used relies on series feedback and terminating networks to induce a stable input reflection coefficient ( a, ω ) with magnitude larger than one at the targeted frequency of.5 GHz [8]. For the associated negative resistance not to induce self-oscillation during the measurement, the Nyquist stability condition also needs to be satisfied. That is, care must be taken that the load-line does not circle the device line. As we shall see this is readily achieved for a 5 Ω source impedance if the device line stays clear of the region neighboring the center of the Smith Chart. A drain voltage of.v and gate voltage of.55v yielding a drain current of 7mA are applied to the device for its DC biasing. The terminating network is implemented with a transmission line resonator. Series feedback was implemented using a shorted stub with a capacitor tap for tuning. The tuning is needed to set the maximum magnitude of the reflection coefficient to occur at.5 GHz due to the sensitivity of the oscillator circuit. Both the gate and drain bias lines were initially realized using λ/4 high impedance transmission lines, shunt capacitors, and series inductors. A broad band bias tee was later used for the drain biasing, as the λ/4 bias line introduced a short at the nd harmonic which prevented the optimization of the fundamental output power.

2 Termination G D S Series L a b Load Circuit V GS + Feedback + V DS Fig.. Oscillator circuit with series feedback. B. Real-time Multi-harmonic active load-pull system The general diagram of real-time multi-harmonic active load-pull system implemented with the LSNA is shown in Fig.. As shown the RF source (ω ) is connected to the oscillator via Port of the LSNA. The incident wave a injected from the RF source (ω ) and reflected wave b from the oscillator are then measured with the LSNA. During the measurements, the oscillator harmonic response can also be monitored by the spectrum analyzer at the circulator port. To determine the optimal impedance termination for the nd and 3 rd harmonic, the multi-harmonic real-time tuning approach is used. For this measurement, a frequency offset Δω of about KHz is used. In this method an incident wave (see Fig. ) at n ω + Δω is injected in the oscillator network. The reflection coefficient obtained for a given incident power: can be described using: + Δω) = a( nω + Δ ) P inc ( nω ω () jpδω t a( nω + pδω) e p= L ( nω, t) = () jpδω t b ( nω + pδω) e p= In addition to the reflection coefficient, the total output power can be represented by: P = N out, total Pout n, t) n= ( ω, (3) Fig.. Real-time multi-harmonic active load-pull system diagram. III. EXPERIMENTAL RESULTS A. Negative Input Resistance A stable negative resistance is obtained according to the Nyquist stability criteria, when the locus of the load reflection coefficient L (ω) versus frequency is not encircling the inverse of the device reflection coefficient ( a =, ω). Since the setup used in Fig. provides a broadband 5 ohm impedance termination verifying ( ω) <, a stable negative L resistance is then obtained if we have (, ω) > max. The input reflection coefficient can be obtained from both the incident a wave and reflected wave b measured by the LSNA, using: max a, ω) b ( ω) a ( ) (5) ( = ω The amplitude of the input reflection coefficient ( a, ω ) versus frequency measured from GHz to 3GHz with the LSNA in its network analyzer mode is shown in Fig. 3. The tuning capacitor and the length of the stubs were adjusted for the negative resistance to peak in the desired frequency range. As a result, a magnitude of 3.7 is observed at.5ghz in Fig. 3. where we define P out (nω,t) as: P out ( nω, t) = { v ( ) nω + pδω p= q= i * ( nω + qδω) e j( p q) Δωt } (4)

3 in P L (mw) frequency (GHz) Fig. 3. Magnitude of Г (,ω) versus frequency. B. Harmonic Tuning The LSNA greatly simplifies the measurement procedure as both the incident wave a and reflected wave b are measured by at the oscillator non-linear circuit reference plane. The output power delivered to the load can be then calculated using: P L ) b ( ω ) a( ) ( ω = ω (6) To increase the maximum output power of the oscillator, harmonic real-time tuning method is applied. A comparison of the output power obtained versus incident power is given in Fig. 4. Initially the output power at the fundamental frequency was obtained by using a λ/4 high impedance bias line connected to the drain. For this measurement, a 5Ω termination is used for the nd harmonic load impedance. As a result, an output power of 3.8mW is obtained. Since the λ/4 bias line provides an open termination at the fundamental it also implements a short at the second harmonic preventing any further nd harmonic optimization from the load circuit. To address this problem the broad band bias tee provided by the LSNA was then used to allow tuning with the nd harmonic. As can be seen in Fig. 4, the impact of the bias tee is quite significant as the output power is increased to 3.mW. The load impedance at the fundamental frequency which provides the maximum output power P L,max can then be identified using:, opt ( ω ) = [ (, opt, ω ) L a ] (7) a (dbm) Fig. 4. Comparison of output powers versus incident power. A maximum output power (P L,max ) of 3.8mW (green dotted line) is obtained with the λ/4 drain bias tee. With a broadband drain bias tee, P L,max increases to 3.mW (red dashed line). Using both recursive RTALP and power sweep, a maximum output power of 38.8mW is obtained with 9.dBm a (blue solid line) Inf Fig. 5. Loci of Г L (ω, t) obtained from the real-time active load-pull measurement by LSNA using (). A frequency offset of about KHz is used. While keeping this optimum Г L (ω ), real-time active load-pull technique was applied to find the optimum Г L (ω ) which provides maximum output power. For this measurement, a ω +Δω signal is injected from the RF source (ω ) and.5ghz signal is injected from the RF source (ω ). Fig. 5 shows the loci of Г L (ω, t) obtained from the RTALP measurements. TABLE I COMPARISON OF THE MEASURED OUTPUT POWERS Method Output power ω ω (mw) Г L.Opt(ω ) Г L (ω ). 3. Г L.Opt(ω ) RTALP(ω ) Г L.Opt(ω ) Г L.Opt(ω ) Г L.Opt(ω ) Г L.Opt(ω )

4 4 The output power contour plot in the Г L (ω ) plane is depicted in Fig. 6. This output power contour plot is generated based on (4) with the loci of Г L (ω ). As can be seen, the maximum output power of 39.5mW is obtained although this is slightly affected by memory effect due to the phase sweeping Inf C. Device line A trajectory plot of the device line a, ω ) obtained with ( (blue top line) and without (red bottom line) the optimum Г L.Opt(ω ) is shown in Fig. 7. The black arrow indicates the direction of increased incident power. The later is swept from -5dBm to 4dBm in step of dbm. The bottom (red) line is initially obtained from the power sweep using a 5 Ω load termination for the nd harmonic. The red dot gives the optimum load Г L.Opt(ω ) = which provides the maximum output power of 3.mW for 8.dBm of incident power. The top (blue) line is measured after applying the optimum nd harmonic termination Г L.Opt(ω ) obtained from the RTALP measurements. The blue dot locates the optimum load Г L.Opt(ω ) = which provides the maximum output power of 38.8mW with the incident power of 9.dBm. As can be seen, the location of the device loadline is slightly shifted when using the optimum load termination Г L.Opt(ω ) for the nd harmonic. Fig. 6. Output power contour plot in the Г L (ω ) plane, obtained from the RTALP measurement by LSNA. The black dot indicates the optimum nd harmonic load impedance (Г L.Opt(ω ) = 68) which maximizes the output power (39.5mW) Keeping the optimum nd harmonic Г L (ω ) and fundamental Г L (ω ) reflection coefficients constants, the circuit was re-measured with the LSNA using constant phase measurements. For this measurement instead of the ω +Δω signal, a ω signal with a proper phase is applied to the oscillator. As a result, a maximum output power of 38.3mW is obtained. This constant phase measurement is more reliable than the RTALP measurement since the later one does not account for memory effects in the transistor. By fixing the nd harmonic load impedance to this optimal value, a new output power versus incident power can be re-measured which accounts now for the nd harmonic termination. As shown in Fig. 4, the maximum output power of the oscillator is increased finally from 3.mW to 38.8mW. A new optimum value of Г L (ω ) which provides this maximum output power is also obtained from this measurement. The optimum 3 rd harmonic load impedance was also determined using RTALP measurement. However, the third harmonic was found to have a negligible impact on the maximum oscillator output power. A comparison of the measured output powers obtained for active load-pull and constant phase for various measurement conditions is given in Table. Note that a subsequent power sweep at ω determined the new optimal termination Г L.Opt(ω ) giving a maximum output power of 38.8mW for the optimal nd harmonic load termination Г L.Opt(ω ) used Inf Fig. 7. Trajectory plot of the device line ( a, ω) versus the incident power P inc = a(ω ) for two different measurement conditions. IV. VERIFICATION OF KUROKAWA THEORY A. Self Oscillation Measurement System To verify the relevance of the device line ( a, ω ) for realizing an oscillator using the Kurokawa theory a self-oscillating circuit is tested. The schematic and pictures of the experimental test bed used for the self-oscillation measurement is shown in Fig. 8 and Fig. 9. The broadband bias tee of the LSNA is used for the drain bias in this test. The total loss including tuner (.8 db) and bias tee + LSNA coupler + cable (6.9 db) losses adds up to 7.7 db.

5 5 Fig. 8. Test bed used for the self-oscillating measurement. ( a, ω) is measured with the LSNA at.5ghz by sweeping the incident power from -5dBm to 4dBm (red line) while keeping Г L (ω ) =.43. which is approximate ω termination provided by the tuner. The black dot indicates the expected operating point at Г L (ω ) = ( a, ω) = of the oscillator at.5 GHz. This operating poi nt yields a power of 8.3mW (4.5dBm) as shown in Fig.. Note that Nyquist requirement at a = for starting the oscillation with the load tuner, forced the selection of an operating point below the maximum power point in Fig P L (mw) 5 5 Fig. 9. Picture of the oscillator with tuner and LSNA. A load tuner is used to set the targeted reflection coefficient at.5 GHz. However, the impedance of the nd harmonic could not be controlled in this self-oscillating test bed but was verified to be around Г L (ω ) =.43.. The device line ( a, ω ) is therefore re-measured for this constant nd harmonic termination a (dbm) Fig.. Output power verses a calculated from LSNA measurements. The black dot gives the predicted output power of 8.3mW (4.5dBm) at the operating point a (.dbm) obtained in Fig. at.5 GHz. B. Experimental Results of self oscillation Self oscillation is finally verified using a load tuner and spectrum analyzer in Fig. 8. Harmonic powers including nd and 3 rd harmonics are shown in Fig. (a) while Fig. (b) shows a magnified version of the fundamental output power Inf TABLE II COMPARISON OF PREDICTED AND MEASURED OSCILLATION FREQUENCY AND HARMONIC POWERS Kurokawa Theory Measured Fig.. Loci of the device line ( a, ω) and the load line Г L (ω ) of the tuner used to realize the self-oscillating oscillator. Fundamental Frequency Fundamental power.5 GHz.55 GHz 4.5 dbm (8.3mW) 4. dbm (5.6mW) nd Harmonic power. dbm -3.9 dbm 3 rd Harmonic power -9.8 dbm dbm Both the load line L (ω) and the device line ( a, ω ) are plotted in Fig.. In this measurement, Г L (ω ) is swept from GHz to 3GHz (blue arrow). The device line

6 6 V. CONCLUSION This paper presents a large-signal measurement-based methodology to design oscillators using the Kurokawa theory. Stable negative input resistance of a.5ghz HEMT oscillator was measured versus frequency and power using a large signal network analyzer. To our knowledge this is the first report of the measurement of the device line ( a, ω) using a LSNA. Previous device line measurements were reported by W. Wagner and P. Berini [6], [9], []. The LSNA greatly simplifies the measurement procedure as the incident and reflected power are readily measured by the LSNA. Further the amplitude and phase of the harmonics is acquired enabling to sweep the impedance termination for the nd and 3 rd harmonics using real-time active load-pull. (a) (b) Fig.. Result of spectrum analyzer measurements. The test bed contributes a loss of 7.7 db to be added to the measured power. As shown, the observed frequency of self oscillation is.55 GHz. Accounting for the loss from the test bed (6.9dB) and tuner (.8dB) an oscillator s output power of 4.75dBm is obtained. This output power is in reasonable agreement with the predicted output power of 4.5dBm in Fig., considering that the nd harmonic load impedance is only controlled approximately in this self-oscillating test bed. A comparison of predicted results from Kurokawa theory using LSNA measurements and Spectrum Analyzer measurements of the self-oscillating oscillator circuit is summarized in Table II. The test bed used attenuates the signal by 7.7, 8.7 and 6.6 db at ω, ω, and 3ω. REFERENCES [] B. Razavi, RF Microelectronics, Prentice Hall, 998. [] K. Kurokawa, Microwave Solid State Oscillator Circuits, Addison-Wesley, Second edition, 968. [3] J. Mukherjee, P. Roblin, and S. Bibyk, An analytic circuit-based model for white and flicker phase noise in LC oscillators, Accepted for publication in IEEE Transactions on Circuits and Systems, 7. [4] M. Vehovec, L. Houselander, and R. Spence, On oscillator design for maximum power, IEEE Transaction on Circuits and Systems, Vol. 5, No. 3, pp. 8-83, Sep [5] V. M. T. Lam, P. C. L. Yip, and C. R. Poole, Microwave oscillator design with power prediction, Electronics Letters, Vol. 7, No. 7, pp , Aug. 99. [6] P. Berini, M. Desgagne, F. M. Ghannouchi, and R. G. Bosisio, An experimental study of the effects of harmonic loading on microwave MESFET oscillators and amplifiers, IEEE Transaction on Microwave Theory and Techniques, Vol. 4, No. 6, pp , Jun, 994. [7] X. Cui, S. J. Doo, P. Roblin, G. H. Jessen, R. G. Rojas, and J. Strahler, Real-time active load-pull of the nd and 3 rd harmonics for interactive design of non-linear power amplifiers, 68 th ARFTG Conference Digest, pp.4-49, Boulder, Colorado, Nov. 6. [8] A. P. Venguer, J. L. Medina, R. A. Chavez, A. Velazquez, A. Zamudio, and G. N. Il in, Theoretical and experimental analysis of resonant microwave reflection amplifiers, Microwave Journal, Vol. 47, No., Oct. 4. [9] W. Wagner, Oscillator design by device line measurement, Microwave Journal, Feb [] G. Gonzalez, Microwave Transistor Amplifiers, Analysis and Design, nd Edition, Prentice Hall, 984.