A Novel requency Independent iultaneous Matching Technique for Power Gain and Linearity in BJT aplifiers Mark P. van der Heijden, Henk. de Graaff, Leo. N. de Vreede Laboratory of Electronic oponents, Technology & Materials ETM DIME Microwave oponent Group MG, Delft University of Technology P.O. Box 505, 2600 GB Delft, The Netherlands Phone: +1 (0)15 278499 ax: +1 (0)15 262216 E-ail: M.P.vanderHeijden@its.TUDelft.nl Abstrac econd-haronic control is ipleented in a balanced coon-eitter configuration to facilitate frequency independent third order interodulation distortion (IM) cancellation. Experients deonstrated an over 15 db iproveent in the output third-order intercept point (OIP). Keywords interodulation distortion, linearity, LNA, power atch I. INTRODUTION Today s arket for high dynaic-range low-noise aplifiers (LNAs) is doinated by bipolar devices for wireless counication systes. This is, due to their high transconductance at low current levels and their relative good noise perforance. Bipolar devices are in general strongly non-linear due to their exponential nature. In view of this, when considering the increasing deands on linearity by today s obile counication standards, people trade off linearity against collector current. Theoretically, it can shown that it is possible to obtain a frequency-independent third-order interodulation distortion (IM) cancellation at low collector currents. IM cancellation exists due to the interaction of the total series resistance (source, base, and eitter) with the exponential base-eitter conductance [1]. In practice, however, this effect is asked when the device is operated at R frequencies, where reactive coponents of the device and the circuit coe doinant [2]. In other work [] partial IM canceling was reported at higher frequencies, which has en attributed to the interaction of the base-eitter diffusion capacitance and the exponential current relationship. More recent work [4] also includes the contribution of the base-eitter depletion capacitance to the high-frequency non-linear havior of a cooneitter stage but does not focus on IM canceling effects. This work provides a theory and a circuit concept for a full frequency span IM cancellation at low collector currents, without trading off any power gain and noise perforance. The circuit concept, in which a balanced configuration is used, also provides orthogonality in the atching requireents for power gain and linearity. ecion II establishes the theory for the full frequency-span IM cancellation using Volterra series analysis. The theory is verified using haronic balance siulations on a stripped Guel Poon odel of a Philips BG410W double poly transistor ( f T = 22 GHz). inally, an IM-copensated balanced Eaplifier circuit was built and easured to support the theory of ection II. II. IM ANALYI O A E TAGE In order to obtain an expression for IM as function of collector current I we use a Volterra series analysis. irst we will calculate the full expression and identify the requireent for low frequency IM-cancellation. or the initial analysis we use the non-linear sall-signal odel in ig.1 of a bipolar transistor in a cooneitter (E) configuration. v (t) v I B Q d Q t I v O (t) ig. 1. all-signal odel of a coon-eitter stage. and L are the source and load ipedance respectively. We assue that the transistor is biased in the active region for which the exponential distortion is doinant and quasi-saturation is not yet present. In this L 409
case, the predoinant source of distortion is the nonlinear exponential base-eitter junction. The base current IB = I / β and the diffusion charge Qd = τ I are linearly related to the collector current I by eans of the current gain β and the forward transit tie τ. The exponential non-linearities can expressed as a Taylor series expansion as given by Eq. (1): i () t = gv () t + g v () t + g v () t c,2, i () t = gv () t + g v () t + g v () t b π π,2 π, q () t = v () t + v () t + v () t d d d,2 d, in which the Taylor coefficients are: I I 1 I g 1 I g g = =, g,2 = =, g, = = v V 2! v 2V! v 6V 2 T T T g g g g =, g =, g = π π,2 π, 2 β 2βVT 6βVT g = τ g, = τ, = τ d d,2 d, 2 2VT 6VT g, (1) [ ] or our initial analysis we assue for the oent, that the base-eitter depletion capacitance t is linear in order to keep the coplexity of the equations included in this paper anageable. ince this is not entirely correct for a forward biased junction, we will consider this atter at a later stage. The Volterra series is calculated sybolically by nodal analysis [5] using Maple V [6]. We consider v (t) and v O (t) to the input and output signal voltage of the syste with v (t) ing a two-tone signal of the for v () t = V cos( ωt) + cos( ω t). or this case, the thirdorder Volterra kernel at the interodulation frequency 2ω ω ) coes: ( H ( jω, jω, jω ) = 1 2 2 T [ ] gl 1 + (2 jω1 jω2) t T( jω1, jω1, jω2) = 6 V N ( jω ) N( jω ) N( jω jω ) N(2 jω ) N(2 jω jω ) 1 g g where T( jω1, jω1, jω2) = 1 2 + β β ( )( ) 2 t t + 2 jω1( jω1 jω2) 2τ g + τ g + (2) g + ( jω1 jω2) t τg 1+ 2 + β g + 2jω1 + 2 g β ( τ ) t t 2 g and N( jω) = 1 + + jω( τg + t) β The agnitude of the IM product at frequency 2ω ω ) can calculated as follows: ( 4 IM = H( jω1, jω1, jω2) V () Eq. (2) shows that there is a real part in T( jω1, jω1, jω2), which only depends on resistive eleents, and an iaginary part, which depends both on resistive and capacitive eleents and on the secondorder interodulation frequencies (2 ω 1) and ( ω1 ω2). The other factor in the nuerator only depends on the depletion capacitance and the source ipedance at the IM frequency. Therefore, this ter can only cancel for a single frequency if the source ipedance is inductive [4]. Yet, to obtain the requireents for frequency independent IM cancellation, we first set the frequency in Eq. (2) and () to zero which reduces IM to: g gl 2 1 β = IM V 5 2 g 8VT + 1 β (4) Hence, Eq. (4) yields the known condition for the source ipedance for IM cancellation at low frequencies [1]: β βvt = = (5) 2g 2I ubstitution of (5) in (2) yields the second requireent for frequency-independent IM cancellation: I t = 2τg = 2τ (6) V In fact, if both requireents are et, a perfect frequency independent cancellation is obtained of the real and iaginary part of T( jω1, jω1, jω2). According to this theory, the current level is fixed for high frequency cancellation for a given intrinsic bipolar transistor by the value of t and τ. onsequently, (5) and (6) reduce to a single requireent for : βτ T = (7) t Note, that ore freedo can obtained by placing a linear capacitor in parallel with the base-eitter depletion capacitance or by scaling the lateral 410
diensions of the device. To deonstrate the theory, we apply a HB siulation in AD to copute the output third-order intercept point (OIP) versus I at different frequencies using an idealized odel (see ig. 1). ig. 2 shows the circuit of the E-stage and the BG410W paraeters used in the odel. The IM cancellation requireent for the source ipedance is = 1500 Ω according to Eq. (7). V LH B VBE bc Q1 VE LH B L I 20 aa β 150 τ 4 ps t 400 f 60 f bc ig. 2. ingle stage coon eitter aplifier. ig. a shows the coputed OIP versus I of the circuit in ig. 2. It can observed that the OIP is independent of center and delta frequency. are still soe other non-linearities, which were not taken into account yet (e.g. the non-linear base resistance). econdly, the established conditions in (7) and (8) are not really convenient for having a conjugate power atch at the input and output of the device. urtherore, the bias circuitry is also part of the load and source ipedance. This eans that if we would like to apply the proper source and load ipedances according to the cancellation requireents, the eleent values for B and L H should go to infinity to obtain full frequency span IM cancellation. A way to circuvent the probles related to atching, is to ake use of a balanced Estage aplifier with a center-tapped transforer for even haronic control at the input. III. THE BALANED E-AMPLIIER ig. 4 shows the novel balanced E-aplifier configuration. In this configuration the requireents for power atch and linearity can established siultaneously without interference of the bias circuitry. V T1 V BE jc Q1 V E T2 L R jc Q2 ig. 4. Balanced E-aplifier stage with IM-cancellation. (a) (b) ig.. OIP versus I of the noral E-stage (a) and the balanced E-stage (b) at different two-tone frequencies. In the previous calculations we did not consider the influence of the collector-base depletion capacitance bc. If we add this capacitance to our odel, the analysis yields an extra IM cancellation requireent for the load ipedance L : τ L = RL = (8) t In reality we will not have perfect frequency independent cancellation. This can attributed to the device itself and the circuit environent. irst of all, the bipolar device is not as ideal as in ig. 1. In a real device we also have the non-linearity of the depletion capacitance t and the contributions of the forward and reverse Early effects, which deteriorate the exponential havior of I. As a result, the peaking of the OIP axiu will soewhat reduced. Besides that, there We already showed in Eq. (2) that the IM cancellation copletely depends on the proper loading of the second-order products. In a balanced configuration we can discriinate tween even and odd-order frequency coponents. Hence, for the second-order coponents at the input of the transistor, R is the ipedance seen at the source-side that establishes IM- cancellation. or the fundaental coponents, the source and load conditions can now chosen arbitrarily, e.g. for noise-atch or power atch. or the balanced situation the requireent for linearity can translated to: R βτ = 2( + ) t bc (9) Note that in this case also the load requireent (8) disappears. This is caused by the effective short-circuit condition for the even haronics at the output of the transistors. onsequently, by using the Miller approxiation bc transfors to the input and adds up with t as indicated in ig. 4. 411
ig. b shows the OIP versus I for the balanced circuit using the ideal-odel (including bc ). The coponent values are = L = 50 Ω and R = 650 Ω. We see that the OIP is still frequency independent, but also independent of and L. An iproveent of over 20 db of OIP can achieved in theory copared to a noral balanced E-aplifier at low collector currents. To support this theory, a hybrid ipleentation has en designed which is discussed in the next section. IV. EXPERIMENTAL REULT ig. 5 shows a photo of the balanced E-aplifier using two BG410W transistors with center-tapped transforers at the input and the output of the aplifier. The transforers have an ipedance ratio of 4. Additional transforer baluns are placed in front of the center-tapped transforers to ensure perfect phase balance over a wide frequency range. As can observed fro the experiental results in ig. 6, pronounced support has en found for the developed theory. This is stressed even ore by coparing the results for the sae circuit with and without the second-haronic control-resistor R. An iproveent of over 15 db in OIP can obtained by applying the correct resistor value R. To verify the effect of the linearization technique at higher powers, ig. 7 shows the fundaental output power versus input power together with IM and IM5 versus power. It shows an iproveent of IM in excess of 20 db and IM5 of over 10 db over wide range of input powers. VBE VE R in out BG410W Transforers ig. 5. Hybrid ipleentation of the balanced E-aplifier. Note that the IM cancellation is based on the proper terination of the second-order products. Therefore, the bandwidth of the transforer ust cover the range of f as well as the double frequency 2f. ince the transforers were liited to approxiately 1 GHz, twotone easureents were perfored at f = 85 MHz and f = 225 MHz in a 50 Ω -environent. ig. 6 shows the OIP versus the D-current. The optiu R -value was calculated to 600 Ω, in which the base resistance and parasitic capacitances were taken into account. ig. 6. Measured OIP versus the total D current I at f = 225 MHz and at f = 85 MHz for different tone spacing f. ig. 7. Output power of the fundaental (black) versus input power together with IM (red) and IM5 (blue) versus power at f = 85 MHz, f = 1 MHz, and V = 1.5 V. This result proves that this circuit concept can extend the spurious free dynaic range draatically. In future work we will concentrate on the integration of IM copensated balanced E configurations utilizing robust biasing [2] techniques. This will facilitate low cost, low power, high dynaic range bipolar LNAs. V. ONLUION A novel design technique has en presented which focuses on the design of highly linear, low power receiver front-ends. The technique utilizes exponential IM canceling by proper terination of the second-order products facilitating orthogonal OIP and ipedance or noise atching. The experiental data is in agreeent with the developed theory and deonstrated over 15 db iproveent of OIP yielding a draatic iproveent in dynaic range at low D power consuption. AKNOWLEDGMENT The authors wish to thank the support of the people in 412
D-N developent of Philips eiconductors in Nijegen, the Netherlands. urtherore, the author wishes to acknowledge Prof. Dr. J. N. Burghartz for his advisory role and prootor of this work. REERENE [1] J. Reynolds, "Nonlinear Distortions and Their ancellation in Transistors," IEEE Trans. On Electonic Devices, no. 11, pp. 595-599, Nover 1965. [2] G. V. Kliovitch, "On Robust uppression of Third-Order Interodulation Ters in all-ignal Bipolar Aplifiers," 2000 IEEE MTT- Int. Microwave yp. Dig., vol. 1, pp. 477-479, June 2000. []. A. Maas, B. L. Nelson, and D. L. Tait, "Interodulation in Heterojunction Bipolar Transistors," IEEE Trans. On MTT, vol. 40, no., pp. 442-448, March 1992. [4] K. Leong ong and R. G. Meyer, "High-requency Nonlinearity Analysis of oon-eitter and Differential-Pair Transconductance tages," IEEE Journal Of ol. tat. ir., vol, no. 4, pp. 548-555, April 1998. [5] P. Wabacq and W. ansen, Distortion Analysis of Analog Integrated ircuits. Norwell, MA: Kluwer, 1998. [6] Maple V Language Reference Manual. New York: pringer- Verlag, 1991. 41