1 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 IN L 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 ΓIN (a1 = 0,ω ) . 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 + Δω is injected in the oscillator network. The 0 termination verifying ΓL (ω ) ≈ 0 < Γmax , a stable negative reflection coefficient obtained for a given incident power: −1 resistance is then obtained if we have ΓIN (0,ω ) > Γmax . The 2 1 input reflection coefficient can be obtained from both the Pinc ()() nω0 + Δ ω = 2 a1 nω 0 + Δ ω (1) incident a1wave and reflected wave b1 measured by the LSNA, using: can be described using: ΓIN (,)()()a1 ω = b1 ω a 1 ω (5) SSB jpΔω ⋅ t ∑ a1( nω 0 + p Δ ω) e p=− SSB ΓL (,)nω0 t = (2) SSB jpΔω ⋅ t The amplitude of the input reflection coefficient ∑ b1( nω 0 + p Δ ω) e p=− SSB ΓIN (,)a1ω 0 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 Pout, total = ∑ Pout (,) nω0 t , (3) Fig. 3. n=1 where we define Pout(nω0,t) as: SSB SSB P(,) nω t = − 1 {(v nω+ p Δ ω) out 0 2 ∑∑2 0 p=−− SSB q= SSB (4) * j() p− q Δω t ×i2 ( nω0 + q Δ ω) e } 3 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.