1Department of Electronic Engineering ... In recent years, the market of wireless communication ... amplifiers (PAs) are used in RF front-ends for their low cost.
Novel Stabilization Method for Eliminating Oscillation in RF CMOS Nonlinear Power Amplifiers Chuande Zhi1,2, Student Member, IEEE, Huazhong Yang1, Senior Member, IEEE, Rong Luo1 1 Department of Electronic Engineering Tsinghua University, Beijing 100084, China 2 The Second Artillery, Beijing 100085, China
Abstract—This paper presents a novel stabilization method for eliminating oscillation in RF CMOS nonlinear power amplifiers. By system identification technique, large signal stability information comes out. Then a band-stop feedback network is introduced in the first stage of power amplifier designed for 802.11b application. This two-stage power amplifier implemented with UMC 0.18um CMOS technology is stabilized by this novel method without the cost of other performance degradation.
I.
INTRODUCTION
In recent years, the market of wireless communication has grown significantly. Radio-frequency (RF) CMOS power amplifiers (PAs) are used in RF front-ends for their low cost and their ability of integration with digital baseband circuits. Most PAs are designed with multi-stage topology which is prone to instabilities. Especially within gain compression regime, many facts give rise to all kinds of oscillations. Linear oscillation is mainly induced by DC bias circuits or match circuits while parametric oscillation is associated with input drive level, load impedance and work frequency. Conventional techniques based on small signal k factor could not analyze the oscillation in PAs. Therefore, large signal stability analysis methods are required. Many papers have presented to analyze the stability of PAs in GaAs pHEMT [1], LDMOS [2], and GaN HEMT [3] technology process. However, the stability analysis of RF CMOS on-chip nonlinear PAs is scarcely discussed. This paper describes a novel stabilization method for eliminating both linear and parametric oscillation in RF CMOS PAs. It uses nonlinear steady state harmonic balance (HB) method to achieve input-output large signal stability parameter. Meanwhile, return rations of each stage for multi-stage power amplifier are used to obtain complete stability information. Finally, a band-stop feedback network placed in the first stage is introduced to make the complete PA stable. II.
resistance looking into the transistor is positive, no oscillation is observed. These stabilities can be analyzed by linear methods proposed by Bode [4] and Platzker [5]. Even though the amplifiers work perfectly stable under small signal conditions, oscillations may occur as the amplifier is driven harder. Such oscillations are referred to as parametric oscillations because they depend on variations of particular external parameters such as bias, frequency and input drive. Elimination of parametric oscillations is necessary for system to work properly. The nonlinear stability analysis can be carried out by perturbation analysis of the periodic steady state [6] [7], as shown in Fig. 1. Once the closed loop frequency response is obtained, system identification methods are applied to determine the system poles and zeros, and then the stability of the steady state solution comes out [7]. This method is illustrated with a CMOS power amplifier designed for IEEE 802.11b system. Design goals are 23dBm output power with more than 25dB small signal gain. The process technology is the UMC 0.18um CMOS 1P6M for Mixed/RF application. Two stages topology is used to realize above specifications. Since all circuit nodes share the same characteristic equation, the poles are independent of the particular location of the current perturbation. However, some circuit node can be numerically less sensitive than others, and exact pole-zero cancellations may occur at some current perturbation locations. Thus, the need for the initial consideration of different observation nodes arises. In this paper, the current VDD
Input match network Large Signal RF input ( Harmonic Balance )
VDD
Inter-stage match network
Output match network
current perturbation
STABILITY ANALYSIS
Linear oscillations appear when the circuit is biased without RF signal input. Under small signal conditions, if the
Figure 1. Simplified large signal nonlinear analysis with current perturbation
This work is sponsored by NSFC under Grant #60025101 and #90307016
0-7803-9584-0/06/$20.00©2006 IEEE.
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perturbation is shifted from output network (Fig.1) to the position shown in Fig. 2.
error can be given by ∧
ε (k ,θ ) = y (k ) − y (k | θ )
When a small signal current perturbation i p is injected into a circuit node, the input admittance is also the corresponding close-loop frequency response achieved by sweeping the frequency of this perturbation current. It is given by:
H close ( jω ) = where
ip
v p is the corresponding output voltage.
In order to get more robust system identification results we select state space model which is described by:
x(k + 1) = A( p, b) x(k ) + B ( p, b)u (k | i p ) y (k ) = C ( p, b) x(k ) + D( p, b)u (k | i p )
(2)
x(k ) , y (k ) and u (k | i p ) are state vector, output vector and input vector respectively. Here p and b denote the input RF power and bias values respectively. A( p, b) , B ( p, b) , C ( p, b) , and D( p, b) are model parameters. can
describe
above
VN (θ , Z N ) =
model
1 N
N
∑ l (ε ((k ,θ ))
parameters
(4)
k =1
∧
θN
is then
∧
θ N = arg min VN (θ , Z N )
(5)
Here arg min means “the minimizing argument of the function”. This method is called prediction-error identification methods (PEM). When 6-order state space PEM model is used, identification results H si ( jw) are perfectly coincident with origin data H close ( jw) , as shown in Fig. 3. After further calculation, a pair of complex conjugate 7 9 poles 6 × 10 ± j1.3 × 10 ( Hz ) are located on the righthand side of the complex plane in conditions of VDD=1.8V and Pin=-20dBm, as shown in Fig. 4. III.
where
θ ∈ { A, B, C , D} .
N
where l (⋅) is a scalar function. The estimated defined by minimization of (4):
Circuit stability information needs to be extracted from the obtained close-loop function. To do so, the Nyquist criterion may be applied to. However, it has an important drawback related to the fact that the number of unstable zeros of close-loop function is generally unknown. The nonencirclement of the origin cannot guarantee the stability of the system if the number of unstable zeros is unknown. Therefore, a different approach is proposed, which does not require any priori knowledge of unstable zeros. It is system identification methods that are used to obtain the transfer function according to the circuit frequency response.
We
When the data set Z = [ y (1), u (1)," y ( N ), u ( N )] is known, we use the following norm:
(1)
vp
(3)
STABILIZATION METHODS
In this section, we present a prototype power amplifier with the UMC 0.18um RF CMOS technology. A stability technique of RF power amplifier, valid for both large signal and small signal regimes, is presented.
as
A good model should produce small prediction errors when applied to the observed data y ( k ) [12]. The prediction Port Vbias 1
Port VDD
Port Vbias 2 Port Out
Port In
current perturbation
Figure 3. Close loop frequency response and its system identification
Figure 2. Position of perturbation current source in this paper
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Port Vbias1
Port VDD
Port Vbias 2 Port Out
stability network
Port In
current perturbation
Figure 5. Band-stop feedback stabilization network Figure 4. Unstable poles obtained by system identificaiton
14
10
K
K
12
6 4
R
m2
2
8 6 4
0
2
-2
0
m2
factor analysis with 2.4GHz input signal
(Left) before stabilization
(Right) after stabilization
frequency and bias conditions are same, poles with positive real part appear if input drive level is -20dBm before stabilization. As presented in [10], with input drive level increasing, poles with positive real part move to negative real axis. The -10dBm input drive level is the bifurcation point. In this condition, a pair of complex conjugate poles
[9]. The frequency division by two is related to sub-harmonic instabilities, as shown in Fig. 4. This oscillation frequency component at 1.3GHz arises with 2.4GHz the input drive. It is necessary to use large signal s parameter to compute k factor by injecting a small signal into the circuit. Considering the output stage transistor being consisted of many parallel multi-finger parameter cell (PCELL), the stabilization network is placed in the first stage, as shown in Fig.5. This network is a band-stop filter network for eliminating linear oscillations and parameter oscillations. In addition, stability analysis around 2.4GHz is insufficient to guarantee stable operation for RF PA. Out of band stability must also be analyzed. After stabilized, the PA is stable in rang from DC to 5GHz, as shown in Fig.6. The modified k factor is suitable for both large signal and small signal stability analysis, and it is dependant on bias, work frequency and input drive level. It comes from stead state solution with HB method and is different from small signal linear k factor. System identification techniques can help to find the stability trend. As shown in Fig. 7, if the RF input signal
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Figure 7. Movement of poles position (Top) before stabilizaiton (Bottom) zoomed-in after stabilization
5.00G
4.50G
4.00G
3.50G
3.00G
2.50G
2.00G
1.50G
1.00G
500.M
5.00G
4.50G
k
4.00G
Figure 6. Stability
3.50G
3.00G
2.50G
2.00G
1.50G
1.00G
500.M
It is well known that a primary contributor to subharmonic oscillations is the nonlinearity of C gs and Cgd [8]
8
0.000
zeros appear in right half plane.
10
R
m2 RFfreq= 1.700E9 permute(K)=1.108 RFpower=-10.000000
14
m2 RFfreq= 2.000E9 permute(K)=0.753 RFpower=-20.000000
0.000
To use properly stabilization procedure for PAs, an understanding of the oscillation mechanism is necessary. The stability method with k factor is severely limited in many cases because the analysis does not hold if the unloaded circuits contain poles or zeros in the right half plane. Therefore, a modified statement of the two port stability criteria involving k factor should be: An unloaded two port which has no poles or zeros in the right half plane will remain stable when loaded externally at its input and output if and only if k > 1 and Δs < 1 for all ω . But most PAs are often driven so hard that they give rise to negative real part impedance or admittance due to the nonlinear capacitances C gs and C gd . It means that poles or
16
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supposed to be tested in May, 2006. V.
CONCLUSION
In this paper, a novel stabilization method is presented for eliminating oscillation in RF CMOS nonlinear PAs. By using system identification technique, large signal stability information is achieved. Then a band-stop feedback network is introduced in the first stage of the PA designed for 802.11b application. This two-stage PA implemented with UMC 0.18um CMOS technology is stabilized by this novel method without the cost of other performance degradation. ACKNOWLEDGMENT
Figure 8. Performance of the PA presented in this paper Solid line is before stabilization; scatter dot is after stabilizaiton
± j1.3 × 109 ( Hz ) locates at image axis. When the circuit is driven harder, all poles move into left half plane. If this PA is driven at level 0dBm, for example, a pair of complex 8 9 conjugate poles −1.7 × 10 ± j1.3 × 10 ( Hz ) lies in left half plane. The position change of poles shown in Fig.7 is the result of bifurcations, which can be used to show stability variations. After the PA is stabilized, all poles lie in left half plane. It is in good agreement with the information from k factor shown in Fig.6. By applying above novel stabilization network and large signal analysis method, the performance of this PA is without the cost of other performance degradation. Small signal gain decreases only about 2dB and output power decreases less than 1dB. Performance is almost unchanged within nonlinear regime, as shown in Fig.8. IV.
LAYOUT
Except for output match network, most components including input match network are integrated on the same chip, as shown in Fig.9. Considering the ground bounce and current hold capability, more than ten ground pads and more than ten supply pads are used in the layout. In addition, onchip inductors are placed far away from transistors in order not to interfere with signal. The chip occupies about 1.5mm ×1.5mm area and has been taped out for manufacture. It is
The authors would like to thank HJTC corp. for chip fabrication. Thanks are also due to Chinese Academy of Sciences EDA center for their multi-project wafer service. REFERENCES [1]
L. Samoska, K.Y. Lin, H. Wang, “On the stability of millimeter-wave power amplifiers”, IEEE MTT-S Digest 2002. [2] F. Wang, A. Suárez, and D.B. Rutledge, “Bifurcation analysis of stabilization circuits in an L-Band LDMOS 60-W power amplifier”, IEEE Microwave and Wireless Components Letters, Vol.15, No.10, October 2005. [3] K.S. Boutros, P. Rowell, and B. Brar, “A study of output power stability of GaN HEMTs on SiC substrates”, IEEE 42nd Annual International Reliability Physics Symposium 2004 [4] H. W. Bode, “Network analysis and feedback,” in Amplifier Design. New York: Van Nostrand, 1945. [5] A. Platzker and W. Struble, “A rigorous yet simple method for determining stability of linear N-ports networks,” in GaAs IC Symp. Dig., 1993, pp. 251–254 [6] A. Anakabe, J.M. Collantes, J. Portilla, “Analysis and elimination of parametric oscillations in monoliticpower amplifiers”, IEEE MTT-S Digest 2002. [7] J. Jugo, J. Portilla, A. Anakabe, “Closed-loop stability analysis of microwave amplifiers”, IEEE Electronics Letters, Vol.37, No.4, 15th February 2001. [8] D. Teeter, A. Platzker, “A compact network for eliminating parametric oscillations in high power MMIC amplifiers”, IEEE MTTS Digest 1999 [9] S. Mons, J.C. Nallatamby, “A unified approach for the linear and nonlinear stability analysis of microwave circuits using commercially available tools”, IEEE MTT-T, Vol.47, No.12, December 1999 [10] S. Jeon, A. Suárez, and D.B. Rutledge, “Global stability analysis and stabilization of a class-E/F amplifier with a distributed active transformer”, IEEE MTT-T, Vol.53, No. 12, December 2005 [11] M. Milev, R. Burt, “A tool and methodology for AC-stability analysis of continuous-time closed-loop systems”, IEEE Proceeding of the Design, Automation and Test in Europe Conference and Exhibition 2005. [12] Lennart Ljung, System Identification—Theory for the User, Prentice Hall, 1999
Figure 9. Layout of the PA presented in this paper
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