Bandwidth of PSK modulated signal
With no filtering or pulse shaping what you have is your signal with the default rectangular pulse shape
$$
\Pi(t) = \begin{cases}1 &amp; \text{for} &amp; -\frac T2\leq t\leq \frac T2\\0 &amp; \text{otherwise}\end{cases}
$$
Where $T$ is the symbol duration. The Fourier transform of the such a pulse result in a sinc function of the form
$$
H(f) = T\operatorname{sinc}\big((f-f_c)T\big) \equiv T\frac{\sin\big(\pi (f - f_c)T\big)}{\pi \left(f-f_c\right)T}\tag{1}
$$
The zeros in Equation $(1)$ are at
\begin{align}
(f - f_c)T &amp;= k\quad \big\vert \quad k\in \mathbb{Z}_{\neq 0}\tag{with $f\neq f_c$}\\
\implies 2(f - f_c) &amp;= 2kR_s\tag{2}
\end{align}
The sinc function in Equation $(1)$ dies slowly resulting in infinite frequency content. Hence the choice of other practical pulse shaping filters such as the SRRC for bandwidth conservation (and ISI mitigation). In brief, having rectangular pulses one has remnant lobes outside the bandwidth of interest whilst with practical ones such as the SRRC you get high attenuation outside the main bandwidth.
For bandpass modulated signals (e.g. PSK) the required double-sided bandwidth is defined as
$$
W_{\rm DSB} = (1 + \alpha)R_s\quad,\qquad 0 \leq \alpha \leq 1
$$
Where $\alpha$ is the roll-off of the raised-cosine pulse, a measure of excess bandwidth, and $R_s$ the symbol rate.
For bandpass systems, the null-to-null bandwidth is defined as
$$f_2 − f_1\tag{3}$$
where $f_2$ and $f_1$ are the first nulls of the magnitude spectrum $|H(f)|$ above and below $\arg\max_\limits f\left(|H(f)|\right)$ respectively. So, from Equation $(3)$ and $(2)$ you have that
\begin{align}
\arg\max_\limits f\left(|H(f)|\right) &amp;= f_c\\
\left(f_2 - f_1\right) = 2(f - f_c) &amp;\equiv 2R_s\tag{with $k = 1$}\\
\end{align}