The progressive retirement of conventional power plants is decreasing the total system inertia and making the frequency control more delicate. In this context, voltage-sensitive loads will have a more pronounced impact on frequency. Therefore, there is an interest in understanding and quantifying how voltage dynamics impact the frequency response. For this purpose, a linearization of the system and the analysis of the obtained transfer functions are in focus. The paper aims to complement the traditional eigenvalue analysis, capture a system's response to large disturbances, and estimate the frequency overshoots. The study also shows that controllers affecting the load voltage, such as Power System Stabilizers (PSSs), can impact frequency response during a large disturbance. The impact of PSS on system responses and its transfer functions is carried out by applying a general control configuration. Both conventional PSS1A and multi-band PSS designs are analyzed and compared. Thereby, the paper explicitly interlinks a PSS design, and its parameters with properties of the system's frequency response reflected in the system transfer function. Illustrating enhancements facilitated by the presented approach, the explicitly derived PSS designs demonstrate the potential to reduce frequency overshoot. As an example, this reduction is achieved by improving a common mode damping or changing the position of the dominant zero of the closed-loop system.