Broadband Variable Passive Delay Elements Based on an Inductance Multiplication Technique Ehsan Adabi, and Ali M. Niknejad Department of Electrical Engineering and Computer Sciences University of California at Berkeley, Berkeley, CA 94720 Abstract— A new technique for making broadband and vari- able passive delay elements is described. By introducing a variable inductance structure and using it along with available varactors, synthesized transmission lines are implemented with variable delay while maintaining a constant Zo over the line bandwidth. Inductance tuning is realized through the effect of mutual inductance. As a demonstration prototype, a single unit cell and two cascaded unit cells were implemented in 90nm digital CMOS process. Delay values ranging from 14ps – 40ps were obtained from DC to 8GHz while maintaining matched condition over the bandwidth with delay variations of less than ±%5. These delay cells could be used in broadband impulse- based beamforming systems to provide variable delays in each RF path. Index Terms—Phase shifter, passive delay element, variable delay, synthesized transmission lines, inductance tuning, induc- tance multiplication. I. I NTRODUCTION Delay elements are important building blocks of numer- ous circuits and systems such as broadband beamforming antenna arrays, delay locked loops, delay based oscillators, and equalizers. Accuracy, tunability and immunity to process- voltage-temperature variations are key performance metrics in designing delay cells. Various forms of active and passive delay elements have been used previously [1]- [3]. In systems using active delay elements, the delay accuracy is maintained through a feedback system and accurate external reference. Active delay cells could be realized in small footprints but they dissipate power and have limited bandwidth whereas passive delay lines could be accomplished with high bandwidth and good accuracy determined by inductances and capacitances that are highly accurate compared to active delay elements. The inductance value is mainly a function of lateral di- mensions of an inductor which is determined by a pre- cise lithographic process. Inter-digitated MOM (Metal-Oxide- Metal) finger capacitors using multiple layers of metals and exploiting intermediate via capacitances are quite precise. These structures are immune to process variation due to the large amount of inherent averaging done on small local capacitances in comprising the desired capacitor. Unlike active delay cells, passive elements are largely independent of voltage and temperature variations. A new method to obtain broadband and tunable delay out of synthesized transmission lines based on an inductance multiplication technique is introduced in this paper. In section II we discuss different types of passive delay structures. Section III focuses on the inductance multiplication technique. Implementation and measurement results are presented in section IV. II. PASSIVE DELAY LINES As shown in Fig. 1a, the most straightforward way to implement a delay element is to use a transmission line. To create a variable delay, multiple transmission lines of different length can be switched into the signal path. On-chip transmission lines are highly accurate, completely linear and very broadband. However they consume large amount of chip area, and are therefore too costly for commercial applications below 10GHz. To decrease the size, artificial transmission lines can be used. In these synthesized transmission lines, lumped inductors and capacitors mimic the role of distributed inductance and capacitance in a real transmission line. The conventional way to make the delay of a synthesized transmission line tunable is by means of varactor loading (Fig. 1b). Varying the line capacitance changes the wave velocity and hence the delay (T D = √ LC) of the line. However this comes at the expense of changing the line’s characteristic impedance (Z o =  L C ). To maintain good return loss, delay variations of only a small fraction of the nominal delay is acceptable. To overcome the Z o variation problem, in [4] a variable capacitor is added in series with the inductor (Fig. 1c). By varying this capacitance, the effective reactance of the series LC circuit is altered. This effective reactance tunability compensates for the Z o variation caused by the change of capacitance values in shunt varactors. Since in this technique a series LC network is emulating the effect of a variable inductor, its functionality is limited to a small bandwidth, and therefore is suitable for narrowband signals. To make an artificial varactor loaded transmission line work with wideband signals, the actual inductance value should be adjusted instead of the effective series reactance, as shown in Fig. 1d. If both series inductance and shunt capacitance are tunable, the delay could be varied while maintaining constant Z o . In the next section, various techniques to realize tunable inductors are described and their advantages and disadvantages are highlighted. III. I NDUCTANCE MULTIPLICATION Inductance is determined by the geometry of a closed path of current and the permeability (μ) of the surrounding 978-1-4244-1808-4/978-1-4244-1809-1/08/$25.00  2008 IEEE 2008 IEEE Radio Frequency Integrated Circuits Symposium RTU1E-1 445