Negative Input Resistance and Real-Time Active Load-Pull Measurements of a 2.5Ghz Oscillator Using a LSNA

Negative Input Resistance and Real-time Active Load-pull Measurements of a 2.5GHz 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, #[email protected]

The multi-harmonic real-time active load-pull technique Abstract—A large-signal measurement-based methodology to introduced by [7] using an LSNA is applied here to the design oscillators using the Kurokawa theory is presented in this characterization of the 2.5GHz oscillator. The LSNA paper. Measurements of the negative input resistance and device remarkably simplifies the entire measurement process. The test line of a 2.5GHz HEMT oscillator versus frequency and power, oscillator circuit and the LSNA test bed are presented in section and its optimization using real-time active load-pull (RTALP) for the 2nd and 3rd harmonics are performed with a large signal II. Measurement results obtained for the oscillator with this test network analyzer (LSNA). As a result, the maximum output bed are reported in section III. Finally a self oscillating circuit power of the oscillator is increased from 31.0mW to 38.8mW. implemented with a load tuner is demonstrated in section IV Finally self-oscillation is verified using a load tuner to yield an and a summary of this work’s achievement is given in section output power and frequency of oscillation in reasonable V. agreement with the Kurokawa analysis.

Index Terms—Real-time Active load-pull, large signal network analyzer (LSNA), negative input resistance, oscillators II. MEASUREMENT SET-UP DESCRIPTION

A. Oscillator Design I. INTRODUCTION The oscillator realized with an ATF54143 HEMT from scillators are essential components of radio frequency Agilent is shown in Fig. 1. The HEMT oscillator circuit used O (RF) transceivers in wireless communication systems. relies on series feedback and terminating networks to induce a Typically RF oscillators are used together with mixers for stable input reflection coefficient ΓIN a ω01 ),( with magnitude frequency translation [1]. In order to design an optimal larger than one at the targeted frequency of 2.5 GHz [8]. For oscillator, it would be greatly beneficial to be able to measure the associated negative resistance not to induce self-oscillation its device line (non-linear device impedance versus oscillation during the measurement, the Nyquist stability condition also amplitude). The later ones can be used in turn to optimize the needs to be satisfied. That is, care must be taken that the output power and the phase noise characteristics of the load-line does not circle the device line. As we shall see this is oscillator [2], [3]. readily achieved for a 50 Ω source impedance if the device line By finding the optimal embedding network of the oscillator stays clear of the region neighboring the center of the Smith at the fundamental frequency, the output power can be Chart. maximized [4], [5]. However, a poor selection of harmonic load A drain voltage of 2.0V and gate voltage of 0.55V yielding a impedances could degrade the performance of the oscillator. A drain current of 27mA are applied to the device for its DC study of the effect of the second harmonic load impedance as biasing. The terminating network is implemented with a well as the device line characterization has been reported using transmission line resonator. Series feedback was implemented active load-pull measurements [6]. The reported measurements using a shorted stub with a capacitor tap for tuning. The tuning indicate the importance of the harmonic load impedances in is needed to set the maximum magnitude of the reflection optimizing the oscillator’s output power and efficiency. In this coefficient to occur at 2.5 GHz due to the sensitivity of the work we present a real-time active load-pull system which oscillator circuit. greatly reduces the acquisition time and facilitates the sweeping Both the gate and drain bias lines were initially realized using of the harmonic phases while recording the RF and DC λ/4 high impedance transmission lines, shunt capacitors, and characteristics at each phase setting. 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 2nd harmonic which prevented the optimization of the fundamental

This work was supported in parts by a National Science Foundation grant. output power. 2

Series ΓΓ LIN

D Load Termination G a1 Circuit S b

Feedback 1

+ V + VDS GS − −

Fig.1. Oscillator circuit with series feedback.

B. Real-time Multi-harmonic active load-pull system The general diagram of real-time multi-harmonic active Fig. 2. Real-time multi-harmonic active load-pull system diagram. load-pull system implemented with the LSNA is shown in Fig. 2. As shown the RF source (ω0) is connected to the oscillator via Port 1 of the LSNA. The incident wave a1 injected from the III. EXPERIMENTAL RESULTS RF source (ω0) and reflected wave b1 from the oscillator are then measured with the LSNA. During the measurements, the A. Negative Input Resistance oscillator harmonic response can also be monitored by the A stable negative resistance is obtained according to the spectrum analyzer at the circulator port. Nyquist stability criteria, when the locus of the load reflection nd To determine the optimal impedance termination for the 2 coefficient Γ ω)( versus frequency is not encircling the inverse and 3rd harmonic, the multi-harmonic real-time tuning L −1 approach is used. For this measurement, a frequency offset Δω of the device reflection coefficient IN a1 =Γ ω),0( . Since the of about 200 KHz is used. In this method an incident wave (see setup used in Fig. 2 provides a broadband 50 ohm impedance Fig. 2) at nω Δ+ ω is injected in the oscillator network. The 0 termination verifying L ω 0)( Γ<≈Γ max , a stable negative reflection coefficient obtained for a given incident power: −1 resistance is then obtained if we have Γ ω),0( Γ> . The IN max 2 1 input reflection coefficient can be obtained from both the inc nP 0 ωω =Δ+ 2 na 01 Δ+ ωω )()( (1) incident a1wave and reflected wave b1 measured by the LSNA, using: can be described using:

IN 1 =Γ aba 11 ωωω )()(),( (5) SSB ω⋅Δ tjp ∑ ( 01 Δ+ ωω )epna −= SSBp ΓL ω0 tn ),( = (2) SSB ω⋅Δ tjp The amplitude of the input reflection coefficient ∑ ( 01 Δ+ ωω )epnb −= SSBp ΓIN a ω01 ),( versus frequency measured from 2GHz to 3GHz with the LSNA in its network analyzer mode is shown in Fig. 3. In addition to the reflection coefficient, the total output The tuning capacitor and the length of the stubs were adjusted power can be represented by: for the negative resistance to peak in the desired frequency range. As a result, a magnitude of 3.7 is observed at 2.5GHz in N P ,totalout = ∑ out ω0 tnP ),( , (3) Fig. 3. n=1

where we define Pout(nω0,t) as:

SSB SSB ω tnP ),( −= 1 ({ pnv Δ+ ωω ) out 0 2 ∑∑ 02 =−−SSBp = SSBq (4) * )( Δ− ωtqpj 2 ( 0 Δ+× ωω )eqni }

4 40

3.5 35

30 3

25 2.5

in 20 Γ (mW) L

2 P 15

1.5 10

1 5

0.5 0 2 2.1 2.2 2.3 2.4 2.5 2.6 2.7 2.8 2.9 3 -20 -15 -10 -5 0 5 10 15 frequency (GHz) a (dBm) 1 Fig. 3. Magnitude of ГIN(0,ω) versus frequency. Fig. 4. Comparison of output powers versus incident power. A maximum output power (PL,max) of 23.8mW (green dotted line) is obtained with the λ/4 drain bias tee. With a broadband drain bias tee, PL,max increases to 31.0mW (red B. Harmonic Tuning dashed line). Using both recursive RTALP and power sweep, a maximum The LSNA greatly simplifies the measurement procedure as output power of 38.8mW is obtained with 9.1dBm a1 (blue solid line). both the incident wave a and reflected wave b are measured 1 1 1.5 by at the oscillator non-linear circuit reference plane. The output power delivered to the load can be then calculated using: 1.0 1 0.5 2.0 2 2 1 1 PL ω0 = 2 b ω01 − 2 a ω01 )()()( (6) 0.5 0.2

To increase the maximum output power of the oscillator, 0 0.0 0.2 0.5 1.0 2.0 Inf harmonic real-time tuning method is applied. A comparison of -0.2 the output power obtained versus incident power is given in Fig. -0.5 4. Initially the output power at the fundamental frequency was -0.5 -2.0 obtained by using a λ/4 high impedance bias line connected to -1 the drain. For this measurement, a 50Ω termination is used for -1.0 the 2nd harmonic load impedance. As a result, an output power -1.5 of 23.8mW is obtained. -1.5 -1 -0.5 0 0.5 1 1.5

Since the λ/4 bias line provides an open termination at the Fig. 5. Loci of ГL (2ω0, t) obtained from the real-time active load-pull fundamental it also implements a short at the second harmonic measurement by LSNA using (2). A frequency offset of about 200 KHz is used. preventing any further 2nd harmonic optimization from the load circuit. To address this problem the broad band bias tee While keeping this optimum ГL(ω0), real-time active provided by the LSNA was then used to allow tuning with the load-pull technique was applied to find the optimum ГL(2ω0) 2nd harmonic. As can be seen in Fig. 4, the impact of the bias which provides maximum output power. For this measurement, tee is quite significant as the output power is increased to a 2ω0+Δω signal is injected from the RF source (2ω0) and 31.0mW. The load impedance at the fundamental frequency 2.5GHz signal is injected from the RF source (ω0). Fig. 5 which provides the maximum output power PL,max can then be shows the loci of ГL(2ω0, t) obtained from the RTALP identified using: measurements.

TABLE I −1 COMPARISON OF THE MEASURED OUTPUT POWERS optL ω0, [Γ=Γ a optIN ω0,1 ),()( ] (7) Method Output power

ω0 2ω0 (mW)

ГL.Opt1(ω0) ГL(2ω0) 31.0 0.415∠ 177.8 0∠ 0.0

ГL.Opt1(ω0) RTALP(2ω0) 39.5 0.415∠ 177.8 1∠ 168.0

ГL.Opt1(ω0) ГL.Opt1(2ω0) 38.3 0.415∠ 177.8 1∠ 168.0

ГL.Opt2(ω0) ГL.Opt1(2ω0) 38.8 0.416∠ 171.0 1∠ 168.0 4

The output power contour plot in the ГL(2ω0) plane is C. Device line depicted in Fig. 6. This output power contour plot is generated −1 A trajectory plot of the device line ΓIN a ω01 ),( obtained with based on (4) with the loci of ГL(2ω0). As can be seen, the maximum output power of 39.5mW is obtained although this is (blue top line) and without (red bottom line) the optimum slightly affected by memory effect due to the phase sweeping. ГL.Opt(2ω0) is shown in Fig. 7. The black arrow indicates the direction of increased incident power. The later is swept from

-15dBm to 14dBm in step of 1dBm. The bottom (red) line is 1.0 1 0.04 initially obtained from the power sweep using a 50 Ω load nd 0.5 2.0 0.8 termination for the 2 harmonic. The red dot gives the

0.6 optimum load Г .Opt1(ω ) = 0.415 177.8 which provides the 0.035 L 0 ∠ 0.4 0.2 maximum output power of 31.0mW for 8.1dBm of incident 0.2 power. The top (blue) line is measured after applying the 0.03 nd 0 0.0 0.2 0.5 1.0 2.0 Inf optimum 2 harmonic termination ГL.Opt(2ω0) obtained from

-0.2 the RTALP measurements. The blue dot locates the optimum 0.025 -0.4 -0.2 load ГL.Opt2(ω0) = 0.416∠ 171.0 which provides the -0.6 maximum output power of 38.8mW with the incident power of 0.02 -0.8 9.1dBm. As can be seen, the location of the device loadline is -0.5 -2.0 -1 slightly shifted when using the optimum load termination -1.0 nd 0.015 ГL.Opt(2ω0) for the 2 harmonic. -1 -0.5 0 0.5 1 1.0 Fig. 6. Output power contour plot in the ГL(2ω0) plane, obtained from the 1 nd RTALP measurement by LSNA. The black dot indicates the optimum 2 0.5 2.0 0.8 harmonic load impedance (ГL.Opt(2ω0) = 1∠ 168) which maximizes the output power (39.5mW). 0.6

nd 0.4 0.2 Keeping the optimum 2 harmonic ГL(2ω0) and fundamental 0.2 ГL(ω0) reflection coefficients constants, the circuit was re-measured with the LSNA using constant phase 0 0.0 0.2 0.5 1.0 2.0 Inf measurements. For this measurement instead of the 2ω0+Δω -0.2 signal, a 2ω0 signal with a proper phase is applied to the 0.15 oscillator. As a result, a maximum output power of 38.3mW is -0.4 -0.2 0.1 obtained. This constant phase measurement is more reliable -0.6 0.05 than the RTALP measurement since the later one does not -0.8 0 0.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.20.2 0.5 account for memory effects in the transistor. -0.5 -2.0 nd -0.8 -0.7 -0.6 -0.5 -0.4 -0.3 By fixing the 2 harmonic load impedance to this optimal -1 value, a new output power versus incident power can be -1 -0.5 -1.00 0.5 1 nd −1 re-measured which accounts now for the 2 harmonic Fig. 7. Trajectory plot of the device line ΓIN a ω01 ),( versus the incident termination. As shown in Fig. 4, the maximum output power of 2 power = 1 aP ω )( for two different measurement conditions. the oscillator is increased finally from 31.0mW to 38.8mW. A inc 2 01 new optimum value of ГL(ω0) which provides this maximum output power is also obtained from this measurement. IV. VERIFICATION OF KUROKAWA THEORY The optimum 3rd harmonic load impedance was also A. Self Oscillation Measurement System determined using RTALP measurement. However, the third −1 harmonic was found to have a negligible impact on the To verify the relevance of the device line ΓIN a ω01 ),( for maximum oscillator output power. realizing an oscillator using the Kurokawa theory a A comparison of the measured output powers obtained for self-oscillating circuit is tested. The schematic and pictures of active load-pull and constant phase for various measurement the experimental test bed used for the self-oscillation conditions is given in Table 1. Note that a subsequent power measurement is shown in Fig. 8 and Fig. 9. The broadband bias sweep at ω0 determined the new optimal termination tee of the LSNA is used for the drain bias in this test. The total ГL.Opt2(ω0) giving a maximum output power of 38.8mW for loss including tuner (0.8 dB) and bias tee + LSNA coupler + nd the optimal 2 harmonic load termination ГL.Opt(2ω0) used. cable (6.9 dB) losses adds up to 7.7 dB.

−1 ΓIN a ω01 ),( is measured with the LSNA at 2.5GHz by sweeping the incident power from -15dBm to 14dBm (red line)

while keeping ГL(2ω0) = 0.43∠ 100.0 which is approximate

2ω0 termination provided by the tuner. The black dot indicates −1 the expected operating point at ГL(ω0) = ΓIN a ω01 ),( = 0.56∠ 175.0 of the oscillator at 2.5 GHz. This operating poi nt yields a power of 28.3mW (14.5dBm) as shown in Fig. 11. Note that Fig. 8. Test bed used for the self-oscillating measurement. Nyquist requirement at |a1|=0 for starting the oscillation with the load tuner, forced the selection of an operating point below the maximum power point in Fig. 11.

20 (mW) L

P 15

Fig. 9. Picture of the oscillator with tuner and LSNA. 0 -20 -15 -10 -5 0 5 10 15 a1 (dBm) A load tuner is used to set the targeted reflection coefficient Fig. 11. Output power verses a1 calculated from LSNA measurements. The at 2.5 GHz. However, the impedance of the 2nd harmonic black dot gives the predicted output power of 28.3mW (14.5dBm) at the could not be controlled in this self-oscillating test bed but was operating point a1 (11.2dBm) obtained in Fig. 10 at 2.5 GHz. verified to be around ГL(2ω0 ) = 0.43∠ 100.0. The device line −1 nd ΓIN a ω01 ),( is therefore re-measured for this constant 2 B. Experimental Results of self oscillation harmonic termination. Self oscillation is finally verified using a load tuner and spectrum analyzer in Fig. 8. Harmonic powers including 2nd rd 1.0 and 3 harmonics are shown in Fig. 12 (a) while Fig. 12 (b) 1 shows a magnified version of the fundamental output power. 0.5 2.0 0.8

0.6 TABLE II 0.4 0.2 COMPARISON OF PREDICTED AND MEASURED OSCILLATION FREQUENCY AND HARMONIC POWERS 0.2 Kurokawa Theory Measured 0 0.0 0.2 0.5 1.0 2.0 Inf

-0.2 Fundamental 2.5 GHz 2.515 GHz Frequency -0.4 -0.2 14.5 dBm 14.1 dBm Fundamental power -0.6 (28.3mW) (25.6mW) -0.8 -0.5 -2.0 2nd Harmonic power 1.22 dBm -3.19 dBm -1 -1 -0.5 -1.00 0.5 1 3rd Harmonic power -29.08 dBm -36.8 dBm −1 Fig. 10. Loci of the device line ΓIN a ω01 ),( and the load line ГL(ω0) of the tuner used to realize the self-oscillating oscillator.

−1 Both the load line ΓL ω)( and the device line ΓIN a ω01 ),( are plotted in Fig. 10. In this measurement, ГL(ω0) is swept from 2GHz to 3GHz (blue arrow). The device line 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 2.5GHz 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 −1 of the device line ΓIN a ω01 ),( using a LSNA. Previous device line measurements were reported by W. Wagner and P. Berini [6], [9], [10]. 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 2nd and 3rd harmonics using real-time active load-pull.

(a)

REFERENCES [1] B. Razavi, RF Microelectronics, Prentice Hall, 1998. [2] K. Kurokawa, Microwave Solid State Oscillator Circuits, Addison-Wesley, Second edition, 1968. [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, 2007. [4] M. Vehovec, L. Houselander, and R. Spence, “On oscillator design for maximum power,” IEEE Transaction on Circuits and Systems, Vol. 15, No. 3, pp. 281-283, Sep. 1968. [5] V. M. T. Lam, P. C. L. Yip, and C. R. Poole, “Microwave oscillator design with power prediction,” Electronics Letters, Vol. 27, No. 17, pp. 1574-1575, Aug. 1991. [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 (b) amplifiers,” IEEE Transaction on Microwave Theory and Techniques, Vol. 42, No. 6, pp. 943-950, Jun, 1994. Fig. 12. Result of spectrum analyzer measurements. The test bed contributes a [7] X. Cui, S. J. Doo, P. Roblin, G. H. Jessen, R. G. Rojas, and loss of 7.7 dB to be added to the measured power. nd rd J. Strahler, “Real-time active load-pull of the 2 and 3 harmonics for interactive design of non-linear power As shown, the observed frequency of self oscillation is 2.515 amplifiers,” 68th ARFTG Conference Digest, pp.42-49, GHz. Accounting for the loss from the test bed (6.9dB) and Boulder, Colorado, Nov. 2006. tuner (0.8dB) an oscillator’s output power of 14.075dBm is [8] A. P. Venguer, J. L. Medina, R. A. Chavez, A. Velazquez, obtained. This output power is in reasonable agreement with A. Zamudio, and G. N. Il’in, “Theoretical and the predicted output power of 14.5dBm in Fig. 11, considering experimental analysis of resonant microwave reflection that the 2nd harmonic load impedance is only controlled amplifiers,” Microwave Journal, Vol. 47, No. 10, Oct. approximately in this self-oscillating test bed. 2004. A comparison of predicted results from Kurokawa theory [9] W. Wagner, “Oscillator design by device line using LSNA measurements and Spectrum Analyzer measurement,” Microwave Journal, Feb. 1979. measurements of the self-oscillating oscillator circuit is [10] G. Gonzalez, Microwave Transistor Amplifiers, Analysis summarized in Table II. The test bed used attenuates the signal and Design, 2nd Edition, Prentice Hall, 1984. by 7.7, 8.7 and 6.6 dB at ω0, 2ω0, and 3ω0.