2.5 KiB
Class 03
Non Linear functions with OAs
Multivibrator Has negative and positive feedback, but net positive
Log and AntiLog Amplifier with negative Feedback, but also
Logarithmic Converters Logarithmic / AntiLog (Exponential) Converter
Sound level is given in Decibels, as it is always compared to the sound threshold.
20\log{\frac{P}{P_{0}}}
V_out = -V_{T}*\ln{}
V_o = R_1Ie^{\frac{-V_i}{V_T}}
!
Expression of the above system
$V_in = -R_in * I_in = -Rin*I_sat e^{\frac{E_o}{V_T}}$
\displaystyle E_O = V_T \ln(-\frac{V_in}{R_in*I_sat})
!Class_03 2022-05-03 13.39.51.excalidraw
\begin{flalign}
&V_1 = -V_T\ln{\frac{Vi}{R1*I_{ES}}}&\\\
&V_2 = -V_T\ln{\frac{Vi}{R2*I_{ES}}}&\\
&V_O = -(V_1+V_2)&\\
&V_O = V_T\ln{(\frac{V_{i1}V_{i2}}{(RI_{ES})^2})}&\\
&V_O' = -RI_{es}e^{\frac{V_O}{V_T}}&\\
&V_O' = -\frac{V_{i1}V_{i2}}{RI_{es}}&\\
\\
&V_O'' = V_{i1}V_{i2}&\\
\end{flalign}
$$****
```circuitjs
$ 1 0.000005 10.20027730826997 50 5 43 5e-11
i -192 208 -112 208 0 0.01
a -112 224 16 224 8 15 -15 1000000 10.624172192589858 0 100000
g -112 240 -112 288 0 0
w -112 208 -112 128 0
t 64 176 64 128 0 1 14.983134150394081 15.001062402219262 100 default
t -16 176 -16 128 0 -1 -0.63704611232159 24.98818848248753 100 default
w -112 128 -32 128 0
w -16 176 -16 272 0
w -16 272 96 272 0
r 96 272 96 336 0 1000
g 96 336 96 368 0 0
w 96 272 208 272 0
r 208 272 208 144 0 1000
a 112 144 208 144 8 15 -15 1000000 -14.983134150394081 0 100000
w 0 128 16 128 0
w 16 128 48 128 0
w 16 128 16 224 0
g 64 176 64 192 0 0
i 192 48 112 48 0 0.01
w 112 48 112 128 0
w 80 128 112 128 0
g 112 160 112 208 0 0
g 192 48 224 48 0 0
g -192 208 -224 208 0 0
O 208 144 240 144 1 0
x 235 217 265 220 4 24 R1
x 124 308 154 311 4 24 R2
```
\begin{flalign} &I_1 = I_{es}e^{\frac{V_{BE_1}}{V_T}} \longrightarrow V_{BE_1} = V_T \ln{\frac{I_1}{I_{es}}}&\\ &I_1 = I_{es}e^{\frac{V_{BE_2}}{V_T}} \longrightarrow V_{BE_2} = V_T \ln{\frac{I_2}{I_{es}}}&\\ &V_1 = V_O*\frac{R2}{R1+R2}&\ &V_O = (1+\frac{R1}{R2})V_T\ln{\frac{I_1}{I_2}} \end{flalign}
![[Pasted image 20220503142156.png]]
\begin{flalign} &V_{ref} = R_{ref}I_1 = R_{ref}I_{es}e^{\frac{V_{BE_1}}{V_T}} \longrightarrow V_T\ln{\frac{V_{ref}}{R_{ref}I_{es}}} = V_{BE_1}&\\ &V_O = RI_2 = RI_{es}e^{\frac{V_{BE_2}}{V_T}} \longrightarrow V_T\ln{\frac{V_O}{R_{ref}I_{es}}} = V_{BE_2} &\ &V_1 = V_i \frac{R_2}{R_1+R_2}&\ &V_i = (1+\frac{R_1}{R_2})V_T \ln{\frac{V_{ref}}{V_O}\frac{R}{R_{ref}}}&\ &V_O = \frac{V_{ref}}{} \end{flalign}