From 5bb7c0e3b6cf0851a346a96ce6badbdc6ed4812d Mon Sep 17 00:00:00 2001
From: Martin Kennedy <hurricos@gmail.com>
Date: Mon, 5 May 2025 07:54:38 -0400
Subject: [PATCH] next!

---
 Final.tex | 29 +++++++++++++++++------------
 1 file changed, 17 insertions(+), 12 deletions(-)

diff --git a/Final.tex b/Final.tex
index 26d5b40..08aa44f 100644
--- a/Final.tex
+++ b/Final.tex
@@ -114,23 +114,23 @@ divider, and so
   \frac{v_{out}}{v_{in}} = - \frac{R_2}{R_1+Z_{C_1}}
 \end{equation}
 
-The high-pass filter design is a common one, with a well-known cutoff
+This high-pass filter design is a common one, with a well-known cutoff
 frequency $\omega_c = \frac{1}{R_1 C}$ and gain $K = \frac{R_2}{R_1}$
 \cite{b3}. To acquire a cutoff frequency of
 $\omega_c = \SI{40}{\kHz} \approx \SI{2.51E5}{}$ rad/s,
 $R_1 = \SI{100}{\ohm}$ and $C_1 = \SI{39}{\nano\farad}$ will
 suffice. Only $R_2$ remains to be selected to determine the limit on
 gain; selecting $R_2 = \SI{100}{\kohm}$ yields
-$K = 1000 = \SI{30}{dB}$.
+$K = 1000 = \SI{60}{dB}$.
 
 \subsection{Toward a more perfect Model}
-A more accurate representation of the op-amp foregoes the
-assumption, oft made regarding op-amps wired in a feedback
-configuration, that $v_n = v_p$. Avoiding this assumption requires a
-more precise description of the properties of the op-amp itself,
-describing its input resistance $R_i$, output resistance $R_o$, and
-the relationship between the input and output - the open-loop gain
-$A$. Figure \ref{img:opamp_internal} depicts such a model.
+A more accurate representation of the op-amp foregoes the assumption,
+often made regarding op-amps wired in a feedback configuration, that
+$v_n = v_p$. Avoiding this assumption requires a more precise
+description of the properties of the op-amp itself, describing its
+input resistance $R_i$, output resistance $R_o$, and the relationship
+$A$ between the input and output, also known as the open-loop
+gain. Figure \ref{img:opamp_internal} depicts such a model.
 
 \begin{figure}[h]
   \caption{A more accurate depiction of an op-amp \cite{b2}}
@@ -156,19 +156,24 @@ and input of the op-amp. This measure is useful, as it describes the
 absolute maximum gain performance of the op-amp: notice, for example,
 that the feedback resistor $R_2$ in the selected high-pass filter
 design only serves to limit the gain and has no bearing on the cutoff
-frequency.
+frequency; its value can be increased until the gain is restricted by
+the op-amp itself instead of the resistor (otherwise, an op-amp
+would have infinite gain if it lacked a feedback resistor).
 
 In some cases, manufacturers give more precise details about op-amp
 operation than would be specified under generic ``open-loop gain'':
 for example, the LM741 datasheet documents the \textit{Open-Loop
- Large-Signal Differential Voltage Amplification} as a function of
+  Large-Signal Differential Voltage Amplification} as a function of
 frequency, as seen in Figure \ref{img:lm741_oclsg}. Despite being
 closely related to ``open-loop gain'', it is distinct in that it is
 measured with an output load (in this case, $R_L = \SI{2}{\kohm}$),
 and under conditions such that the load is significant, i.e. that the
 operating output is known to be a meaningful fraction of the supply
 voltage \cite{b1}. Here, it is $V_o = \SI{10}{V}$ for
-$V_{CC} = \pm \SI{15}{V}$.
+$V_{CC} = \pm \SI{15}{V}$. Still, for the purposes of this paper,
+``open-loop gain'' is treated as ``open-loop large-signal differential
+voltage amplification'', with caution made to stay away from
+specifically small-signal measurements.
 
 \begin{figure}[h]
   \caption{The large-signal open-loop gain of the LM741}