We describe linear models of the IDA (International Deployment of Accelerometers) and SRO (Seismic Research Observatories) feedback seismometers obtained by straightforward analysis of the control systems. The most important property of these models is the theoretical transfer function they yield, relating Earth acceleration to output voltage. The parameterization of the theoretical transfer function is described. Several uses of the system models and transfer function are discussed, but we conclude that the parameterized models do not provide a sufficiently accurate means of describing the installed accelerometer's behavior. A speedier, more automatic and more accurate calibration can be obtained by electrically perturbing the seismometer system. This technique is discussed in Part 2.