96 lines
2.5 KiB
Markdown
96 lines
2.5 KiB
Markdown
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# Class 03
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**Non Linear functions with OAs**
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**Multivibrator**
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Has negative and positive feedback, but net positive
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**Log and AntiLog**
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Amplifier with negative Feedback, but also
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**Logarithmic Converters**
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Logarithmic / AntiLog (Exponential) Converter
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Sound level is given in Decibels, as it is always compared to the sound threshold.
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$$
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20\log{\frac{P}{P_{0}}}
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$$
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$V_out = -V_{T}*\ln{}$
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$V_o = R_1Ie^{\frac{-V_i}{V_T}}$
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![[Pasted image 20220503133103.png]]
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Expression of the above system
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$V_in = -R_in * I_in = -Rin*I_sat e^{\frac{E_o}{V_T}}$
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$\displaystyle E_O = V_T \ln(-\frac{V_in}{R_in*I_sat})$
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![[Class_03 2022-05-03 13.39.51.excalidraw]]
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$$
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\begin{flalign}
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&V_1 = -V_T\ln{\frac{Vi}{R1*I_{ES}}}&\\\
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&V_2 = -V_T\ln{\frac{Vi}{R2*I_{ES}}}&\\
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&V_O = -(V_1+V_2)&\\
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&V_O = V_T\ln{(\frac{V_{i1}V_{i2}}{(RI_{ES})^2})}&\\
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&V_O' = -RI_{es}e^{\frac{V_O}{V_T}}&\\
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&V_O' = -\frac{V_{i1}V_{i2}}{RI_{es}}&\\
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\\
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&V_O'' = V_{i1}V_{i2}&\\
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\end{flalign}
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$$****
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```circuitjs
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$ 1 0.000005 10.20027730826997 50 5 43 5e-11
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i -192 208 -112 208 0 0.01
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a -112 224 16 224 8 15 -15 1000000 10.624172192589858 0 100000
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g -112 240 -112 288 0 0
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w -112 208 -112 128 0
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t 64 176 64 128 0 1 14.983134150394081 15.001062402219262 100 default
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t -16 176 -16 128 0 -1 -0.63704611232159 24.98818848248753 100 default
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w -112 128 -32 128 0
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w -16 176 -16 272 0
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w -16 272 96 272 0
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r 96 272 96 336 0 1000
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g 96 336 96 368 0 0
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w 96 272 208 272 0
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r 208 272 208 144 0 1000
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a 112 144 208 144 8 15 -15 1000000 -14.983134150394081 0 100000
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w 0 128 16 128 0
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w 16 128 48 128 0
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w 16 128 16 224 0
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g 64 176 64 192 0 0
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i 192 48 112 48 0 0.01
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w 112 48 112 128 0
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w 80 128 112 128 0
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g 112 160 112 208 0 0
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g 192 48 224 48 0 0
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g -192 208 -224 208 0 0
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O 208 144 240 144 1 0
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x 235 217 265 220 4 24 R1
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x 124 308 154 311 4 24 R2
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```
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$$
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\begin{flalign}
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&I_1 = I_{es}e^{\frac{V_{BE_1}}{V_T}} \longrightarrow V_{BE_1} = V_T \ln{\frac{I_1}{I_{es}}}&\\\
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&I_1 = I_{es}e^{\frac{V_{BE_2}}{V_T}} \longrightarrow V_{BE_2} = V_T \ln{\frac{I_2}{I_{es}}}&\\\
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&V_1 = V_O*\frac{R2}{R1+R2}&\\
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&V_O = (1+\frac{R1}{R2})V_T\ln{\frac{I_1}{I_2}}
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\end{flalign}
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$$
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![[Pasted image 20220503142156.png]]
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$$
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\begin{flalign}
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&V_{ref} = R_{ref}I_1 = R_{ref}I_{es}e^{\frac{V_{BE_1}}{V_T}} \longrightarrow V_T\ln{\frac{V_{ref}}{R_{ref}I_{es}}} = V_{BE_1}&\\\
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&V_O = RI_2 = RI_{es}e^{\frac{V_{BE_2}}{V_T}} \longrightarrow V_T\ln{\frac{V_O}{R_{ref}I_{es}}} = V_{BE_2} &\\
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&V_1 = V_i \frac{R_2}{R_1+R_2}&\\
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&V_i = (1+\frac{R_1}{R_2})V_T \ln{\frac{V_{ref}}{V_O}\frac{R}{R_{ref}}}&\\
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&V_O = \frac{V_{ref}}{}
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\end{flalign}
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$$
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