In the study of mass spectra, extremely sensitive electrometers are necessary for resolving the detection of ions. In this work I model and analyze the performance of a specific transimpedance amplifier presently in use in a mass spectrometer. I use optimal filter theory to find the amplifiers ideal charge measurement threshold, after formulating the contributions of Johnson noise and amplifier input voltage noise. As this work is also intended to serve as an in-depth guide to transimpedance amplifiers, I begin with a short history of these amplifiers and a description of noise in general. A short discussion of the noise found in the ionization chamber of a mass spectrometer is discussed, but not analyzed. The transimpedance amplifier circuit was modeled by RC networks both in feedback and at the amplifier input, in addition to a signal current source, coupling capacitor, and parasitic input capacitance. I determined individual transfer functions and applied them to the various noise terms. At lower frequencies the Johnson noise is found to dominate, whereas at higher frequencies the amplifiers input voltage noise dominates. I represent noise output contributions as ratios to the total noise, ratios to the signal, and in plots. I conclude with a discussion of the impact these sources have on the signal-to-noise ratio, and in relation to the noise figure. I found that, relative to the effect of amplifier input voltage noise by itself, Johnson noise is clearly the dominating factor in the determination of the charge measurement threshold.