700 IEEE MICROWAVE AND WIRELESS COMPONENTS LETTERS, VOL. 15, NO. 10, OCTOBER2005 Wire Bonded Interdigital Capacitor Francisco P. Casares-Miranda, Pablo Otero, Member, IEEE, E. Márquez-Segura, Member, IEEE, and C. Camacho-Peñalosa, Member, IEEE Abstract—Interdigital capacitors (IDCs) are convenient capac- itance devices in microstrip circuits, even if only low capacitance values can be achieved. Nevertheless, undesired resonances de- grade their performance when frequency increases. Short circuits across the end of alternate fingers of the IDC improve its high frequency response by eliminating that drawback. Simulated and measured results are presented. Index Terms—Interdigital capacitor (IDC), microwave pas- sive circuits, wire bonded interdigital capacitor (WBIDC), wire bonding. I. INTRODUCTION R ECENT advances in metamaterial transmission lines and microwave devices have renewed the need and interest in the availability of broadband planar capacitors of high nominal capacitance [1], [2]. Fig. 1(a) shows a microstrip interdigital ca- pacitor (IDC), which is a widely used component to build a few picofarads capacitance in microstrip technology [3], [4]. The equivalent circuit usually employed to model this component is shown in Fig. 1(b). This circuit adequately models the IDC at low frequencies and predicts the series resonance at , as shown in Fig. 1(c). When analyzed with a full-wave EM solver, how- ever, additional resonances at frequencies can be observed as well. If the series capacitance is small enough, then approaches . Otherwise, when a larger value of is needed, the number, or the length, or both, of the fingers of the IDC have to be increased. The length of the fingers can not grow indefi- nitely, it has to be shorter than a quarter guided wavelength [5]. On the other hand, the increment in the number of fingers re- sults in lower frequencies of the undesired resonances. Even if there are only a few fingers, some of the resonant frequencies will be lower than the frequency of the series resonance, that is, . In that case, the IDC performance is degraded because its usable frequency band is shortened, as shown in Fig. 1(c). The IDC is a multiconductor structure, which presents pass- and stop-bands [3], [6]. This work shows how the short circuits across alternate fingers of the IDC improve the high frequency response, because the number of stop-bands is reduced. This improvement is obtained without any diminution in capacitance value. The improvement is demonstrated by numerical analysis and verified with experiments. From now on, the resulting de- vice will be called wire bonded interdigital capacitor (WBIDC). Manuscript received March 31, 2005; revised June 9, 2005. This work was supported by the Spanish Ministry of Science and Technology and by the European Regional Development Funds of the European Union under Grant TIC2003-05027. The review of this letter was arranged by Associate Editor J.-G. Ma. The authors are with the Dpto. Ingeniería de Comunicaciones, E.T.S. In- geniería de Telecomunicación, Universidad de Málaga, Málaga 29071, Spain (e-mail: casares@ic.uma.es). Digital Object Identifier 10.1109/LMWC.2005.856835 Fig. 1. (a) Microstrip interdigital capacitor (IDC). (b) Equivalent circuital model of the IDC. (c) Typical parameters of a series IDC. II. CIRCUITAL MODELS AND FREQUENCY RESPONSE Fig. 1(c) shows typical -parameters of a series IDC. Spu- rious spikes in and can be observed at frequencies , which prevent the IDC to be used beyond the lowest frequency, , where the IDC could still show a capacitive behavior. All IDCs show that problem when designed and built. If the series IDC was considered to be a single series capacitance, the value of that capacitance, , could be obtained from the param- eter of the series IDC by means of (1) where is the reference impedance and is the frequency. Fig. 2(a) and (b) show circuital models of the IDC presented in Fig. 1(a) and of the proposed WBIDC. Considering that it is a short transmission line, a finger can be represented by a se- ries inductance and a shunt capacitance. For the sake of clarity, shunt capacitances are not shown in Fig. 2. Capacitive coupling is modeled by the capacitances , where and are the finger numbers. Inductive coupling can be neglected in a first approx- imation [7]. Bonding wires short circuit alternate fingers, that is, fingers on the same port of the IDC, leading to the simplified equivalent circuit shown in Fig. 2(b). 1531-1309/$20.00 © 2005 IEEE