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.
In this paper, we present a phased-array transceiver chip operating in full X-band (8-12 GHz) in 65-nm CMOS technology. The presented transceiver for the transmit/receive module (TRM) consists of a 6-bit passive phase shifter, a 6-bit attenuator, a bi-directional gain amplifier (BDGA), and a single pole double throw (SPDT) switch connected to the internal power amplifier (PA) and the low-noise amplifier (LNA) to serve as a duplexer. A 64-bit SPI scan-chain is integrated for digital TRM control. The transmitter achieves greater than 15 dB of power gain with 11.84 dBm at the output 1-dB compression point (OP1dB). To achieve a wideband operation of the passive phase shifter, we assigned two different resonant frequencies for the phase leading and lagging networks and aligned the slopes of their phase responses to have the desired phase shifts at the center frequency. The RMS phase error is less than 5 • , and the RMS amplitude error is less than 0.45 dB for all phase and attenuation states within 8-12 GHz while dissipating 216 mW dc power from a 1 V power supply. The receiver shows greater than 15 dB of power gain and has a noise figure (NF) of less than 8.4 dB for the entire X-band. The RMS phase error and the RMS amplitude error are less than 5 • and 0.45 dB, respectively, for all control states within 8-12 GHz. The receiver consumes 110 mW with a 1 V power supply. The transceiver chip occupies an area of 4 × 1.88 mm 2 .
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