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A low voltage and wide tuning range voltage controlled oscillator (VCO) at 2.4 GHz is developed for ISM applications. A design procedure with the parasitics of packaged devices considered is offered. A VCO with a 200 MHz tuning range for less than 2 V using a packaged varactor is demonstrated.
and Chun-Chieh Chien
Institute of Communication Engineering, National Chiao-Tung University
Hsin-Chu, Taiwan, ROC
Designing VCOs with low voltage and wide tuning range is an interesting topic for wireless applications.1,2 For low cost reasons, surface-mount devices are still widely used. In practice, these devices possess parasitics resulting in a self resonant frequency (SRF), compatible with the operating frequency, and causing some complexity in the frequency control. A design methodology, focusing on frequency control and device selection, is presented here. The goal is to build a VCO with a tuning range from 2.3 to 2.5 GHz with a tuning sensitivity larger than 100 MHz/V under low voltage operation (3 V).
Wideband VCOs have been studied by many researchers.38 Also, a number of commercial design software packages are available. In the case of the one-port negative resistance approach of Kurokawa7 , the onset of oscillation must satisfy the conditions where the negative resistance equals the positive external loss and the total reactance is zero. The configuration of a common emitter transistor with a series feedback capacitor is considered here. The required negative resistance is produced from the positive feedback of a capacitor in the emitter terminal. However, the suitable choice of the crucial elements, such as the feedback capacitor and varactor, is not clearly indicated. The problem is that the polarity of the reactance in the feedback arm may be changed and can lead to the disappearance of the negative resistance as the operating frequency exceeds its SRF. Besides, the typical range of capacitance of commercially available varactors using a silicon process varies from 3 to 50 pF at the test voltage (generally 2 V).9 The right choice of varactor is very crucial for design success, especially at low operating voltage. An analytic approach is presented here to obtain the optimum device choice and avoid the parasitics, especially for the varactor and the feedback capacitor. Once the key device properties are determined, the exact frequency of the VCO can be predicted by computer-aided analysis.
The schematic of the VCO with a series feedback capacitor at the emitter terminal is shown in Figure 1. It belongs to the class of Clapp oscillators. Three issues should be considered simultaneously during the design. They are the appropriate region of negative resistance, the tuning ratio (0.2/2.3 GHz = 8.7 percent) and the operating frequency (2.3 to 2.5 GHz). Except for the junction capacitance of the transistor, four elements in the series tank circuit are to be determined, which are the emitter series capacitor Ce , the DC blocking capacitor Cb , the varactor capacitance Cv and the external inductor Lex . Each element has its own parasitic and SRF. In general, the smaller the capacitance, the higher the SRF. Le , Lb and Lv are the equivalent parasitic inductors for Ce , Cb and Cv , respectively, as shown in Figure 2. For simplicity, the small parallel package capacitor( 0.1 pF) in the varactor model is neglected.
Note that the SRF of the capacitor Ce plays an important role in the behavior of the negative resistance. At the frequency of interest, a BJT transistor is represented by an equivalent model with only the junction capacitor Cπ 2Cje0 + gm F and the base resistance rπ taken into account in the input port, where Cje0 is the junction capacitance between base and emitter at zero bias, gm is the transconductance and F is the forward base transit time.10 The input negative impedance is given as8
when rπ >> 1/ωCπ . The real part of Zin is negative at low frequency and increases monotonically with the zero-crossing point in the frequency domain roughly equal to the SRF of Ce . Above the SRF, the negative resistance disappears. Hence, the SRF of capacitor Ce acts as the limit for the negative resistance. It can be easily measured with a network analyzer (HP8753). The dependence of SRF as a function of the capacitance for a typical series of 0603 (= 0.06 x 0.03 in2 ) capacitors (Philips) is shown in Figure 3. The fitted curve satisfies the relation
For 2.5 GHz operation, the capacitor Ce should be less than 5 pF.
It is obvious that the oscillation frequency in the series tank circuit is
The equivalent parasitic inductors Lb and Le in Cb and Ce , respectively, satisfy Equation 2 derived from
The tuning ratio is given as
ΔCeff = variation of the capacitance Ceff as a function of tuning voltage
Because of the series connection, the tuning capability depends on the ratios of Cv , Cπ and Cb to Ce , which is now less than 5 pF. Fortunately, although under low operating voltage, the variation of a varactor capacitance from one to three volts is quite significant. For comparison, the parameters of the equivalent circuit for two typical varactors (Philips BB883 and BB142) are extracted from the one-port scattering parameter S11 and are listed in Table 1. The BB883 device has larger Cv than the BB142 varactor. The ratio of (Cv (1)Cv (3))/Cv (1) is nearly 50 percent in both cases. The notation Cv (V) means the capacitance of varactor at the tuning voltage V. Hence, the tuning ratio is roughly equal to 16.6 percent if Cv (1) = Ce and without the Cπ and Cb effects. The ratio becomes 12.5 percent if Cv (1) = 2Ce . When Cπ and Cb are taken into account, the ratio is reduced. In view of the availability of varactors with small capacitance values (3 pF), the range for the Ce selection is very narrow. In addition, a transistor with larger capacitance C¼ is preferred. Hence, a transistor with medium ft is chosen. Figure 4 shows the dependences of the tuning ratio as a function of the emitter capacitor Ce for the BB142 and BB833 varactors, respectively, with Cπ = 4.58 pF and two different Cb (10 and 100 pF). Cπ = 4.58 pF is taken from a typical UHF transistor at low current operation (5 mA), such as BFS520 with Cjeo = 1.245 pF and F = 8.61 ps. The figure shows clearly for the varactor BB142 that the capacitor Ce has a large degree of freedom from approximately 2 pF (mark P or Q) to 5 pF. However, for BB833, the useful range is small from 4 pF (mark X) to 5 pF. Even the case with Cb = 10 pF is impractical because the crossing point (mark Y) is over 5 pF.
The operating frequency is achieved by trimming the external inductor Lex . However, the equivalent parasitic inductors from Cb and Ce and solder pads may lead to an impractical value of Lex . These inductors are absorbed as parts of the external inductor. Because Lb is slightly proportional to Cb , Lex is given from Equations 2 and 3 as
K0 = constant 13.6π from Equation 2
For the BB142 varactor the useful range of Lex is under 3 nH (mark R or S), while the required inductance for BB833 is nearly equal to zero (mark Z). Zero inductance is an impractical value for circuit realization. It implies that a varactor with large ratio Cv(1)/Ce (2 here), which would lead to the disappearance of the negative resistance, is not applicable in this case.
DESIGN PROCEDURE AND RESULTS
Based on the previous study, a procedure for the design of a wide tuning VCO is offered. First, Ce is chosen with its SRF slightly higher than the required upper limit (2.5 GHz). A transistor with medium ft is chosen to give the proper junction capacitance C¼ . As for Cb , a trade-off between quality factor and tuning ratio is made. The larger the Cb , the wider the tuning. It leads to a small Lex and thus low quality factor. To obtain a higher Q factor, a choice of Cb >10 Ce is suggested. For the desired tuning ratio, Cv(1) Ce is chosen (BB142). Once all the capacitors are chosen, Lex is trimmed according to Equation 5.
The VCO is designed with the BFS520 transistor and BB142 varactor. Ce = 2 pF and Cb = 40 pF are chosen. The supply voltage is 3 V with a current consumption of 5.5 mA. The fT is approximately 5.5 GHz. The external inductor is obtained from the pad. The tuning capability of the VCO is shown in Figure 5. The phase noise is shown in Figure 6. The output performance is listed in Table 2. It was observed that the grounding point of Ce is indeed crucial for the upper limit. Multiple vias are employed.
In this article, a low voltage, wide tuning VCO with applications to the 2.4 GHz ISM band is presented. The frequency control is clarified by special emphasis on the inherent SRF of the devices. The design procedure starts from selecting the feedback capacitor Ce at the emitter terminal whose SRF is taken to be larger than the highest operating frequency. Once chosen, the other elements in the series tank circuit are determined accordingly. The tuning ratio is closely related to the relative ratio of Cv to Ce . It is concluded that the SRF of capacitor Ce plays an important role in the frequency control and should be carefully chosen for higher frequency applications, such as in the 5.8 GHz ISM band. *
1. M. Zannoth, J. Fenk, A. Springer and R. Weigel, "A Single-chip SI-bipolar 1.6 GHz VCO with Integrated-bias Network," IEEE Transactions on Microwave Theory and Techniques, Vol. MTT-48, February 2000, pp. 203205.
2. P. Shveshkeyev, "A Wideband VCO for Set-top Applications," Microwave Journal, Vol. 42, No. 4, April 1999, pp. 7488.
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5. John Kitchen, "Octave Bandwidth Varactor-tuned Oscillators," Microwave Journal, Vol. 30, No. 5, May 1987, pp. 347353.
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7. K. Kurokawa, "Some Basic Characteristics of Broadband Negative Resistance Oscillators," The Bell System Technical Journal, Vol. 48, July-August 1969, pp. 19371955.
8. U.L. Rohde, Digital PLL Frequency Synthesizers: Theory and Design, Prentice-Hall, NJ, 1983, Chapter 4, pp. 150174.
9. Philips Products Data Book, September 1993.
10. P.R. Gray and R.G. Mayer, Analysis and Design of Analog Integrated Circuit, John Wiley & Sons Inc., New York, 3rd edition, 1997, Chapter 3, pp. 215217.
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