A report describes a non-standard direct digital synthesizer (DDS) implementation that can be used as part of a coherent transponder so as to allow any rational turnaround ratio to be exactly achieved and maintained while the received frequency varies. (A coherent transponder is a receiver-transmitter in which the transmitted carrier is locked to a pre-determined multiple of the received carrier’s frequency and phase. That multiple is called the turnaround ratio.)
The report also describes a general model for coherent transponders that are partly digital. A partially digital transponder is one in which analog signal processing is used to convert the signals between high frequencies at which they are radiated and relatively low frequencies at which they are converted to or from digital form, with most of the complex processing performed digitally. There is a variety of possible architectures for such a transponder, and different ones can be selected by choosing different parameter values in the general model.
Such a transponder uses a DDS to create a low-frequency quasi-sinusoidal signal that tracks the received carrier’s phase, and another DDS to generate an IF or near-baseband version of the transmitted carrier. With conventional DDS implementations, a given turnaround ratio can be achieved only approximately, and the error varies slightly as the received frequency changes. The nonconventional implementation employed here allows any rational turnaround ratio to be exactly maintained.
This work was done by Larry R. D’Addario of Caltech for NASA’s Jet Propulsion Laboratory. NPO-47460
This Brief includes a Technical Support Package (TSP).

Achieving Exact and Constant Turnaround Ratio in a DDS-Based Coherent Transponder
(reference NPO-47460) is currently available for download from the TSP library.
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Overview
The document titled "Achieving Exact and Constant Turnaround Ratio in a DDS-Based Coherent Transponder" is a technical support package from NASA's Jet Propulsion Laboratory (JPL) that outlines the principles and design considerations for coherent transponders. These devices are crucial in modern communication systems, particularly in aerospace applications, where reliable signal transmission and reception are essential.
At the core of the document is a general model for coherent transponders, which are transceivers that maintain a phase-locked relationship between the transmitted carrier frequency (f_T) and the received carrier frequency (f_R). Specifically, the transmitted frequency is a predetermined multiple (R) of the received frequency, expressed as f_T = R f_R. This relationship allows for effective modulation of the carrier with different information in each direction, facilitating complex communication tasks.
The document emphasizes the importance of constraints in the design of these transponders. It discusses the necessity of adhering to the sampling theorem, which dictates that the bandwidth of filters used in analog-to-digital converters (ADCs) and digital-to-analog converters (DACs) must be less than half the sampling rate. Additionally, it highlights the need for certain dimensionless synthesis factors to be rational numbers, often constrained to ratios of small integers for practical implementation.
The analysis also delves into the effects of phase noise from the reference oscillator on the transmitted carrier. It concludes that slow changes in the reference frequency, akin to phase noise at small offset frequencies, do not impact the transmitted carrier frequency, thereby ensuring stability in communication.
The document serves as a comprehensive guide for engineers and researchers involved in the design and implementation of coherent transponders, providing insights into the dynamic behavior of these systems and the relationships between various parameters. It underscores the significance of precise frequency control and the role of digital signal processing in enhancing the performance of transponders.
Overall, this technical support package not only presents a detailed model for coherent transponders but also offers practical guidelines and considerations for their development, contributing to advancements in aerospace communication technologies.

