RF Bandpass Filter Design Using Capacitive Degeneration Alberto Valdes-Garcia, Jose Silva-Martinez and Edgar Sánchez-Sinencio Analog and Mixed-Signal Center, Electrical Engineering Deparment Texas A&M University, College Station, Texas, 77843-3128 E-mail:
[email protected] ABSTRACT
2. IMPEDANCE REFLECTION WITH A CAPACITIVE DEGENERATED TRANSISTOR
This work proposes the use of a capacitively degenerated transconductor to construct an RF bandpass filter. The fundamental theoretical elements for the application of this technique are provided. First, the impedance seen from the source/emitter of a transistor with capacitive degeneration and an LC tank connected at its gate/base is analyzed. The conditions under which this impedance exhibits a large value in a narrow bandwidth are obtained showing good agreement between theoretical and simulated results. A general RF filter structure based on the analyzed active resonant cell is introduced and described with a macromodel. A sample 5.2GHz bandpass filter is designed for a SiGe BiCMOS 0.25µm process. Simulation results for the designed RF filter show S21>6dB, Q>20 consuming 1mA from a 2.5V supply.
Some of the reported RF LC Voltage Controlled Oscillator (VCO) designs are based on the use of capacitive degenerated transistors. In [6], a theoretical analysis is presented to show that an equivalent negative resistance can be seen from the base of a bipolar transistor with capacitive degeneration. This technique has also been demonstrated in a CMOS VCO [7]. In this work, further study into the properties of a capacitive degenerated cell is performed to propose a stable, RF filter structure. Fig. 1 shows the basic circuit under consideration. A bipolar transistor is shown but the following analysis is also valid for a MOS transistor. It is important to note that at GHz frequencies the base-emitter capacitance (Cp) of the bipolar transistor dominates over the base-emitter resistance. In this way, at the frequencies of interest, the same simplified small-signal model topology can be used for both MOS and bipolar transistors.
1. INTRODUCTION Contemporary wireless systems demand increasingly higher levels of integration for the reduction of the form factor and cost of the transceiver modules. One of the remaining bottlenecks for the implementation of a fully integrated radio is the implementation of on-chip RF filters with suitable performance for channel selection, image rejection, etc. Most of the current integrated RF filters make use of available on-chip inductors to form LC resonant tanks. Several techniques have been explored to enhance the Q factor of LC RF filters by compensating the inherent losses of integrated inductors [1-5]. These techniques consist of implementing negative resistance cells with active elements. Different implementations have been demonstrated at GHz frequencies in CMOS [1, 3-5] and BiCMOS [2] technologies. However, further research is required to reduce the power consumption and improve their dynamic range of on-chip RF filters in order to make them suitable for modern practical communication systems.
VDD C Zb
B Cp
gm*VBE E
SImplified Bipolar Transistor Model
Ze Zbp
IB
Cq
GND
Figure 1. Basic capacitively degenerated cell The goal of this analysis is to show that the impedance seen from the emitter of the transistor (Zbp) can be significantly increased at the resonant frequency of Zb through appropriate choice of Cq. The impedance Ze seen from the emitter is:
In this work, the use of capacitive degeneration is introduced as a technique for the design of integrated RF bandpass filters.
0-7803-9197-7/05/$20.00 © 2005 IEEE.
Zo
798
Ze =
Zb ⋅ Cp ⋅ s + 1 gm + Cp ⋅ s
(1)
Then, with the degeneration capacitor Cq:
Zbp =
Zb ⋅ Cp ⋅ s + 1 Zb ⋅ Cp ⋅ Cq ⋅ s 2 + (Cq + Cp ) ⋅ s + gm
(2)
If Zb is a parallel RLC tank with impedance:
Zb =
RLs R + Ls + RLCs 2
(3)
the numerator and denominator of Zbp become
Num(Zbp) = [ R ⋅ L(C + Cp ) ⋅ s + L ⋅ s + R] 2
Figure 2. Denominator of Zbp for Cq=586fF
(4)
Den( Zbp) = R ⋅ L ⋅ (Cp ⋅ Cq + C ⋅ (Cp + Cq )) ⋅ s 3 + (R ⋅ L ⋅ C ⋅ gm + L ⋅ (Cp + Cq )) ⋅ s 2
+ (gm ⋅ L + R ⋅ (Cp + Cq )) ⋅ s + gm ⋅ R
(5)
Zbp can become infinite at some frequency ω if the Den(Zbp) has complex conjugate poles with purely imaginary components. A third order equation in the form: (6)
s3 + a ⋅ s2 + b ⋅ s + c = 0 can be written as:
(s + j ⋅ b )⋅ (s − j ⋅ b )⋅ (s + a ) = 0
Figure 3. Calculated Zbp for different values of Cq
(7)
if ab=c. For Den(Zbp)=0, this condition (ab=c) can be expressed as a second order polynomial of Cq:
(
)
R ⋅ Cq 2 + L ⋅ gm + 2 ⋅ R ⋅ Cp − gm ⋅ R 2 ⋅ Cp ⋅ Cq 2
2
+ R ⋅ L ⋅ C ⋅ gm + gm ⋅ L ⋅ Cp + R ⋅ Cp = 0
(8)
If Cq is a solution of equation 8, Zbp will exhibit a very large value at a frequency given by:
ω=
gm ⋅ L + R ⋅ (Cp + Cq ) ≈ R ⋅ L ⋅ (Cp ⋅ Cq + C ⋅ (Cp + Cq ))
1 L⋅C
(9) Figure 4. Simulated Zbp for different values of Cq
It is important to note that the resonant frequency ω depends mainly on the values of the resonant LC tank and not on Cq. To verify this analysis, a circuit schematic with models from the IBM 6HP BiCMOS 0.25µm technology is built according to Fig. 1. The resonant tank is formed by
L=4.2nH and C=400fF (with a resonant frequency at 3.9GHz). Through Cadence simulations Cp was found to be 90fF and gm=17mA/V. The equivalent R of the physical LC parallel tank was found to be around 1.1KΩ. Substituting the mentioned parameters into equation 8 and
799
VDD
solving for Cq, the optimum values (to achieve a large impedance Zbp) were found to be: 586fF and 851fF. Fig. 2 shows the real and imaginary parts of the denominator in equation 5 for C=586fF. As expected, both the real and imaginary parts of the third order polynomial become zero at the same frequency.
Vb
Lf
Lm
1 gm2
Q1 Ld
Vi+
GND
A possible transistor-level implementation of the proposed RF filter structure is depicted in Fig. 6. The input stage consists of an inductively degenerated bipolar differential pair, which acts as a transconductor and provides input match. A differential version of the discussed active resonant impedance is placed as a cascode load to the input stage. Note that the degeneration capacitance Cq only acts in differential mode, preventing common mode instability. Finally, the differential output current from the collectors of the capacitive degenerated transistors is converted into a voltage at the output matching network formed by Lo and Co. In contrast to other reported RF filter topologies, in this circuit the same dc current is used for both the input stage and the active cell that compensates the loss of the inductor. This feature can lead to a significant reduction in power consumption.
3. SIMULATION RESULTS The proposed RF filter implementation shown in Fig. 6 is designed to operate at 5.2GHz (U-NII band employed for wireless LAN applications) using SiGe BiCMOS 0.25µm technology. S-parameter simulations are run with 50ohm input and output ports and the models from the design kit for the MIM capacitors, on-chip inductors and RF bipolar transistors. The value of Cq is chosen to obtain a Q factor of 20. The simulation results are shown in Figs. 7 through 10. Input match (S116dB) and unconditional stability at all frequencies are obtained using only 1mA from a 2.5V supply. As expected, the Q factor and center frequency can be tuned independently. A summary of the performance of the designed filter is presented in Table 1. The relatively low 1dB compression point is a consequence of the low bias current employed and the moderate signal swing at the collector of the input transistors.
gm2
Cf
Lm
Figure 6. Differential bandpass filter realization
Zo
Rq
Q2
Vb
gm2
Cq
Q1 Ld
Lf
Co
Cq
Vi-
Vout2
Cp
Cf Co
Fig. 5 shows a conceptual representation of the proposed general RF filter structure based on capacitive degeneration. Rq, Cf and Lf represent the lossy LC tank connected at the base/gate of the active device. The capacitively degenerated transistor can be represented by the components Cp (gate-source or base-emitter capacitance), Cq (degeneration capacitance), transconductance gm2 and resistance 1/gm2. If an input transconductor is added (gm1), the input voltage can be applied as a current to the resonant impedance. The output voltage (Vout1) in this case can be taken at the emitter/source of the degenerated transistor. Alternatively, collector/drain current of the degenerated transistor can be collected at an output impedance (Zo in Figs. 1 and 5) as shown with gray lines in Fig. 5. To take the output voltage of the filter at Vout2 adds more flexibility to the design. Even though the frequency response of the discussed resonant impedance does not correspond to a conventional 2nd order or 4th order bandpass filter response (see Fig. 4), the proposed structure can provide a high frequency selectivity. Suitable out of band attenuation can be obtained through the input matching network and/or Zo.
gm1
Lo
Cf Q2
2. RF BANDPASS FILTER DESIGN
Vin
Vo+ Vo-
Lo
Figure 3 shows the frequency response of the calculated impedance Zbp for different values of Cq. The computed values for Cq indeed yield a significantly large impedance. Figure 4 shows the simulation results for the magnitude of Zbp in dB for different values of Cq (in fF). The obtained results are in agreement with the previously discussed analysis. The only major difference is that, the maximum impedance is achieved for only one capacitance value and not 2 as predicted by the theoretical analysis. If the value of Cq is increased beyond the smallest of its two calculated optimum values, the impedance keeps decreasing constantly.
Vout1
Vb
Lf
Figure 5. Macromodel of the proposed filter
800
Table 1. RF Filter Performance Summary Center frequency -3dB bandwidth Peak S21 K stability factor Noise Figure Output 1dB compression point Integrated output noise power within -3dB bandwidth Power consumption Technology
Figure 7. S parameter simulation results
5.2GHz 251MHz 6dB >2 16dB -25dBm -67dBm 2.5 mW 0.25µm SiGe BiCMOS
4. CONCLUSIONS It has been shown that a transistor with capacitive degeneration and an LC tank connected at its gate/base is a suitable resonant structure to form a stable RF filter with independent center frequency and Q-factor tunability. A filter has been designed in BiCMOS 0.25µm technology to illustrate the proposed technique. From the simulation results using realistic component models it can be concluded that, with respect to other reported RF filters implemented in similar technologies (see comparison table in [5]), this type of filter design can potentially yield to a comparable noise performance, a higher frequency of operation and a significantly lower power consumption with the penalty of a lower 1-dB compression point.
Figure 8. Frequency tuning
5. REFERENCES [1] T. Soorapanth and S. S. Wong, “A 0-dB IL 2140 30 MHz Bandpass Filter Utilizing Q-Enhanced Spiral Inductors in Standard CMOS”, Vol. 37, No. 5, May 2002. [2] D. Li and Y. Tsividis, “Design Techniques for Automatically Tuned Integrated Gigahertz-Range Active LC Filters”, IEEE, J. of Solid-State Circuits, Vol. 37, No. 8, Aug. 2002. [3] F. Dulger, E. Sánchez-Sinencio and J. Silva-Martinez, “A 1.3-V 5-mW Fully Integrated Tunable Bandpass Filter at 2.1GHz in 0.35-µm CMOS”, IEEE, J. of Solid-State Circuits, Vol. 38, No. 6, June 2003. [4] A. N. Mohieldin, E. Sánchez-Sinencio and J. Silva-Martinez, “A 2.7-V 1.8-GHz Fourth-Order Tunable LC Bandpass Filter Based on Emulation of Magnetically Coupled Resonators”, IEEE, J. of Solid-State Circuits, Vol. 38, No. 7, July 2003. [5] S. Bantas and Y. Koutsoyannopoulos, “CMOS Active-LC Bandpass Filters with Coupled-Inductor Q-Enhancement and Center Frequency Tuning”, IEEE TCAS-II, Vol. 51, No. 2, Feb. 2004. [6] B. Jung and R. Harjani, “High-Frequency LC VCO Design Using Capacitive Degeneration”, IEEE, J. of Solid-State Circuits, Vol. 39, No. 12, Dec. 2004. [7] B. Jung and R. Harjani, “A Wide Tuning Range VCO Using Capacitive Source Degeneration”, IEEE ISCAS, vol. 4, pp. 145-148, May, 2004.
Figure 9. Quality factor tuning
Figure 10. Gain compression
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