# On Noise Modeling of Capacitive Feedback Transimpedance Amplifiers in CMOS
## 1 Introduction  
In the last decades, numerous works have been published on developing transimpedance amplifiers (TIA) in complementary metal oxide semiconductors (CMOSs) [1]. These circuits are typically used for applications where weak signals from current-mode sensors, such as photodiodes (PD), are to be converted to the output voltage of amplitude sufficient for subsequent processing and analysis. Although mostly known for their usage in optical coupling and optical communication receivers [2, 3], the TIA circuits are also widely employed in other applications, such as the readout of MEMS sensors [4, 5, 6, 7, 8], LIDAR processing [9], miniaturized magnetic resonance systems [10], acoustic wave and ultrasound imaging [11, 12, 13, 14], biosensors [15, 16, 17] and other biological applications [18], spectroscopy [19, 20], etc. Clearly, such a broad range of diverse applications had resulted in contradicting sets of requirements and constraints when it comes to choosing an amplifier design and topology for a particular application. For example, while optical communication systems have pushed the requirements for the amplifiers in the direction of higher-gain-bandwidth products, reduced power consumption and noise are often seen as the major constraints for biological and sensor applications, while the bandwidth of such TIAs can be set as low as just several hundreds of kHz. Thus, there may be no single TIA architecturethat best fits every possible application, and different usage scenarios are likely to benefit from complementary properties of competing TIA designs [21]. The work as presented below was initially motivated by the search for a TIA design suitable for low-noise high-performance optical time-domain reflectometer (OTDR) equipment [22]. Fiber optical networks form the backbone of the modern high-speed Internet as they provide extremely high bandwidth, relatively low power, low signal distortions, and all this at low costs. With a constantly growing demand for new online services, cloud-based applications and streaming services are the drivers for new communication technologies as well as force the providers to work continuously on the ramp-up of the existing network infrastructure. However, rapid development and extension of optical communication networks also require equipment for network installation, monitoring, maintenance, fault analysis, and failure prevention. One of the most popular and commonly used instruments for the assessment of optical line quality is the OTDR instrument mentioned earlier. The operating principle of the instrument is based on the injection of a laser pulse into the fiber, where the line quality or, correspondingly, faults are assessed by performing the time-domain analysis of the recorded pulse reflections caused by the Rayleigh scattering. Similarly to other systems with current-mode sensors, here, the TIA is one of the major building blocks of the instrument's front end, and its performance essentially limits the overall sensitivity of the device. The main parameters of the TIA circuit, such as its transimpedance gain, bandwidth, and noise current, define the major characteristics of the OTDR instrument, such as its dead zone and dynamic range [23]. When designing a TIA, several main parameters of the circuit shall be taken into account. Apart from the power consumption, implementation footprint, and supply voltage, the TIA-specific parameters such as photodetector (PD) capacitance, transimpedance gain, bandwidth, and noise are of major importance. While the PD capacitance is mainly a design requirement, the noise, bandwidth, and gain form a typical set of TIA requirements and the basis for deciding whether the suggested topology fits the target application. Clearly, every meaningful design shall be accompanied by sufficiently detailed models so that the performance of the circuit could be understood without performing extensive numerical simulations.