Theory and Design of Impedance Matching Network Utilizing a Lossy On-Chip Transformer

Abstract

In this paper, we present a study on a transformer-based impedance matching network. We use a simplified transformer model comprising two magnetically coupled coils, which are driven by a source and terminated by a load. The formulae of the load and the source impedance for conjugate matching of both sides of the transformer are presented, and a figure of merit is proposed for the evaluation of the power transfer efficiency of the transformer under conjugate matching conditions. Analytical expressions are provided for constructing the widely used transformer network consisting of a resistive load and a parallel tuning capacitor. To verify the proposed work, we examined various on-chip transformers implemented in 0.18 µm CMOS technology. Simulation and measurement results for a matching network synthesized using the aforementioned analytical expressions corresponded well with the result of analysis for operating frequencies up to 72% of the self-resonant frequency of the transformer. The presented results confirm that the proposed analytical formulae based on the simplified transformer model are useful for the design and optimization of transformer-based impedance matching networks in the microwave and millimeter-wave regimes.

A 21.6dBm CMOS power amplifier using a compact high-k output transformer for X-band application

“…Here Qp/Qs is quality-factor of primary/secondary coil, k is coupling coefficient of coils. It can be seen that high Q and k values lead to high passive efficiency, and a higher efficiency corresponds to a lower loss [33,34]. The loss of TF is mainly related to metal and substrate loss, as well as the mutual coupling.…”

A 25.1 dBm 25.9-dB Gain 25.4% PAE X-band Power Amplifier Utilizing Voltage Combining Transformer in 65-nm CMOS

“…In our previous work, we employed a 1:2 TF at the output stage to obtain a high power-efficiency in the X-band PA design [22]. However, a large transformation ratio (n) typically results in a small mutual coupling factor (k) of the realized TF, which results in a degradation of its efficiency which is proportional to k 2 [30]. Moreover, it is difficult to implement a high-efficiency voltage mode power combiner with n>1 because the long routing path of the secondary coil may reduce its self-resonance frequency (SRF), causing imbalances between the combined signals.…”

“…In the real case, the winding coils composing the TF have their own resistive losses, and the mutual coupling factor is smaller than 1. Typically, a TF can be modeled by its lowfrequency model with 5 parameters including L1, L2, R1, R2, and M standing for the primary and secondary inductances, the primary and secondary resistances, and the mutual coupling inductance, respectively [30]. The effective quality factors of the two TF coils at a specific frequency ω are defined to be Q1= ωL1/R1 and Q2=ωL2/R2.…”

“…Now the three-way PC can be characterized by an equivalent two-port TF whose primary inductance is reduced by three times and secondary inductance is tripled compared to those of the single unit TF composing of the original PC. With this equivalent TF model, we can choose its optimum source and load impedances given by [30]…”

“…Each differential pair of transistors is stabilized by using a couple of capacitors cross-connected between the drains and the gates to enhance the impedance matching capability. The conjugate impedance matching for the push-pull amplifiers using a transformer (TF) was carried out based on the analysis results in [30]. The proposed PA is fabricated in 65-CMOS and it works under a supply voltage of 1.2-V. On measurement, the PA achieves a maximum saturated output power (Psat) of 25.1 dBm and a peak PAE of 25.4% at 10.2 GHz, a peak power gain of 25.9-dB at 9.5-GHz.…”