General Measurement-Based Circuit Model for Symmetrical Four-Port RF Transformers Antti Kallio 1 , Timo Veijola 2 , Janne Roos 2 , Mikael Andersson 3 , and Martti Valtonen 2 1 AWR-APLAC, Espoo, Finland 2 Helsinki University of Technology, Department of Radio Science and Engineering, Espoo, Finland. 3 Nokia Devices, Helsinki, Finland Abstract— An equivalent circuit has been developed for a four- port RF transformer by exploiting the symmetry of the device. The circuit consists of four driving-point admittance RLC networks mutually connected via a transforming circuitry, ensuring the symmetry. The measured 4-port frequency responses are converted to respective driving-point admittances, which are approximated by fitting the values of the lumped equivalent circuit 1-ports. Here, a commercial RF transformer has been modelled. I. INTRODUCTION Transformers are used for various purposes in electronics: baluns, wide-band admittance-matching elements, common- mode chokes, etc. The transformers can be discrete components or they can be integrated onto system-on-chips. The behaviour of such devices is far from that of an ideal transformer; the devices have parasitic capacitances, frequency-dependent losses, and limited coupling factors. The non-idealities dominate the device behaviour especially at high frequencies. Passive component models are needed for circuit simulation tools to aid the design of electronic devices. Numerical data from frequency-response measurements is accurate and adequate for frequency-domain simulations, but it cannot be used in time-domain simulations directly. EM simulations are too heavy and slow for circuit-simulation purposes. Lumped-element macro models with frequency- independent component values, in contrast, are well suited for time-domain simulations, and time and memory consumption is much lower than in full EM simulations. The device data from manufactures is not always sufficient, and it is important to be able to characterize the components in the environment where they will be used. This is ensured by making in-house device measurements, and developing an equivalent circuit that reproduces the measured characteristics with sufficient accuracy. Various methods have been used to model four-port transformers. One is to use the elementary transformer model with winding resistances as a basis for the model and then to add some parasitic admittances between the ports and ports and ground based on the physical structure [1]. Another approach is to use a ladder equivalent with mutual couplings between inductances in each section [2] and to fit the element values to measured frequency responses [3-5], or to obtain them from the physical topology, dimensions, and material parameters [6-7]. In this work, a measurement-based model is derived without any need to know the physical structure of the device. This method is applicable in the modelling of commercial devices, whose dimensions and parameters are not always known. Because the model is completely empirical, the frequency range of the measurement directly determines the valid range of the model. Here, the emphasis is both in building an equivalent circuit for a symmetric 4-port transformer and in the method of extracting the parameters for the circuits from the measured S-parameters. The model for a symmetrical 4- port is composed of a general equivalent circuit. It consists of four driving-point admittance networks and ideal transformers. The admittances represent four different symmetrical ways to connect the nodes of the 4-port to form a 1-port admittance. The transformer circuit used here is an extension of the model for symmetrical 2-ports [8]. II. SYMMETRY IN 4-PORTS The symmetrical connections of 4-port nodes are studied in the following,. The symbol for a 4-port with node numbers and a common ground node is shown in Fig. 1. a) b) Figure 1. a) Cross section of a surface-mount, multilayer type 4-port transformer and b) its symbol showing the node numbers of the ports and the ground node. The S-parameters for a general 4-port are ⎥ ⎥ ⎥ ⎥ ⎦ ⎤ ⎢ ⎢ ⎢ ⎢ ⎣ ⎡ = 44 43 42 41 34 33 32 31 24 23 22 21 14 13 12 11 S S S S S S S S S S S S S S S S S . (1) Symmetry of the 4-port implies the following parameter equalities: 3 1 4 2 0 1 2 4 3 978-1-4244-3896-9/09/$25.00 ©2009 IEEE 371