Description of an active reversible in-phase/quadrature modulator carrying out frequency UDC

Description: The circuit schematic of the UDC consists solely of dispersive components. Two low-frequency series LC resonators, with equal inductances (LA=LB) and capacitances (CA=CB), are connected to two input semi-infinite transmission lines, designated as A and B. These resonators are parametrically coupled to a third high-frequency series LC resonator, which leads to an output line C. The parametric coupling is facilitated by adjusting the mutual inductances M1 and M2 between the left and right resonators at the carrier frequency fc, optimized for frequency conversion at the center frequency of the right resonator. When the circuit operates from left to right, it modulates low-frequency signals at frequency f0 traveling through ports A and B, generating sidebands at frequencies fc ± f0 that propagate along the high-frequency line C. Conversely, when the operation is reversed from right to left, the circuit performs demodulation. The spectral density and response landscape for various spatial channels (or ports) of the UDC circuit as a function of frequency is depicted. Dotted lines illustrate the couplings between different ports, while solid and dashed arrows denote different frequencies and their respective conjugates. The resonance line shapes of the two spatially distinct ports A and B are centered on the case where the incoming signal at f0 is resonant with the center frequency (f0 = fA, B). The two sidebands produced by the UDC on channel C are equally detuned from the pump frequency fc.

The UDC circuit operates by utilizing its dispersive components to achieve effective modulation and demodulation of signals. The low-frequency series LC resonators, characterized by their equal inductances and capacitances, form the foundational elements that interact with the semi-infinite transmission lines. The design ensures that the input signals are optimally coupled to the high-frequency resonator, which is essential for efficient frequency conversion.

The parametric coupling mechanism is crucial for the modulation process. By varying the mutual inductances M1 and M2, the circuit can dynamically adjust its response to the incoming low-frequency signals. This capability is particularly important for generating sidebands, which represent the modulated output signals. The ability to modulate signals traveling through ports A and B results in the creation of sidebands at frequencies that are offset from the carrier frequency, enabling effective communication of information.

In terms of spectral analysis, the response landscape of the UDC circuit reveals the interaction between different ports and their respective frequencies. The resonance characteristics of ports A and B are highlighted, showing how the circuit can be tuned to specific frequencies for optimal performance. The relationship between the input signals and the generated sidebands is illustrated by the resonance line shapes, which demonstrate the circuit's ability to maintain fidelity in signal processing.

Overall, the UDC circuit schematic presents a sophisticated architecture for handling low-frequency and high-frequency signals through the strategic use of resonators and transmission lines, illustrating its potential applications in advanced electronic communication systems.Circuit schematic of the UDC containing only dispersive components. The two low-frequency series LC resonators (with LA=LB and CA=CB) are fed by two input semi-infinite transmission lines, A and B, and parametrically coupled to a third high-frequency series LC resonator leading to an output line C. The parametric coupling is achieved by varying the mutual inductances M1 and M2 between the left and right resonators at the carrier frequency ‰c, which, for optimal frequency conversion, is set at the band centre of the right resonator. When operated from left to right, the circuit carries out the modulation of low-frequency signals of frequency ‰0 travelling on ports A and B to generate sidebands at ‰c ± ‰0 travelling on the high-frequency line C.

It carries out the inverse operation of demodulation when operated in reverse from right to left. b, Spectral density/response landscape for different spatial channels (or ports) of the UDC circuit in a as a function of frequency. The dotted lines represent the couplings between different ports. The solid and the dashed arrows represent different frequencies and respective conjugates. The resonance line shapes of the two spatially distinct ports A and B are centred at. Here we show the case when the incoming signal at ‰0 is resonant with the centre frequency ( ‰0= ‰A, B).

The two sidebands generated by the UDC on channel C are detuned from the pump at ‰c by equal amounts.