TF EIM Chapt3 - Revision history

Foretony: /* Junction Rule */

2015-02-12T16:52:41Z

Junction Rule

2015-02-10T20:20:26Z

2015-02-10T20:17:05Z

Differentiator circuit

2015-02-10T19:11:30Z

Pulse Sharpening

2015-02-10T19:10:22Z

RC >> \tau

2011-02-16T03:33:41Z

2011-02-15T06:23:36Z

Electron Energy Distribution

2011-02-15T06:19:28Z

Electron Energy Distribution

2011-02-15T06:17:13Z

Electron Energy Distribution

2011-02-15T06:14:20Z

Electron Energy Distribution

← Older revision		Revision as of 16:52, 12 February 2015
Line 133:		Line 133:

	:<math>\frac{V_{in}}{R_1} + \frac{d}{dt} C\left( V_{in}\right) = \frac{d}{dt} C\left( V_{out}\right) + \frac{V_{out}}{R} + \frac{V_{out}}{R_1} </math>		:<math>\frac{V_{in}}{R_1} + \frac{d}{dt} C\left( V_{in}\right) = \frac{d}{dt} C\left( V_{out}\right) + \frac{V_{out}}{R} + \frac{V_{out}}{R_1} </math>
−	:<math>\frac{d V_{in} }{dt}+ \frac{V_{in}}{CR_1}= \frac{dV_{out}}{dt} + \frac{(R+R_1)}{CRR_1} V_{out} </math>	+	:<math>\frac{d V_{in} }{dt}+ \frac{V_{in}}{CR_1}= \frac{dV_{out}}{dt} + \frac{(R+R_1)}{CRR_1} V_{out} </math>= constant = <math>\frac{V_0}{CR_1} = \frac{V_0}{\tau_{in}}</math>

@@ Line 61: / Line 61: @@
 : <math>I = C \frac{d V_{in}}{dt}</math>
-The loop theorem for V_{out} :
+The Ohm's Law for <math>V_{out}</math> :
 :<math>V_{out} = IR = \left ( C \frac{d V_{in}}{dt} \right ) R = RC \frac{d V_{in}}{dt}</math>

← Older revision		Revision as of 20:17, 10 February 2015
Line 1:		Line 1:
	=Differentiator circuit=		=Differentiator circuit=

−	Consider the effect of a ~~low~~-pass filter on a rectangular shaped input pulse with a width <math>\tau</math> and period <math>T</math>.	+	Consider the effect of a high-pass filter on a rectangular shaped input pulse with a width <math>\tau</math> and period <math>T</math>.

← Older revision		Revision as of 19:11, 10 February 2015
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−	[[File:TF_EIM_PulseSharpnr.png\| ~~200~~ px]]	+	[[File:TF_EIM_PulseSharpnr.png\| 400 px]]

	==Junction Rule==		==Junction Rule==

@@ Line 105: / Line 105: @@
 :<math>\Rightarrow V_{out} = V_{in}\left (1 - e^{-t/RC} \right) = V_{in} \frac{t}{RC} = \frac{1}{RC} \int_0^t V_{in} dt</math>  The circuit appears to be integrating the input voltage.
-If <math>RC << \tau</math> then very little integration is done because the pulse is change at a low frequency compared to the RC constant.
+If <math>RC << \tau</math> then very little integration is done because the pulse is changing at a low frequency compared to the RC constant.
 =Pulse Sharpening=

@@ Line 146: / Line 146: @@
 For the two common semi-conductors of Germainum and Silicon at room temperature we have
-:<math>N_{cb}^{\mbox{Ge} = 1.5 \times 10^{13} electrons/cm^3</math>
+:<math>N_{cb}^{\mbox{Ge}} = 1.5 \times 10^{13} electrons/cm^3</math>
-:<math>N_{cb}^{\mbox{Si} = 8.6\times 10^{9} electrons/cm^3</math>
+:<math>N_{cb}^{\mbox{Si}} = 8.6\times 10^{9} electrons/cm^3</math>
 [[Forest_Electronic_Instrumentation_and_Measurement]]

@@ Line 130: / Line 130: @@
-The total number of electrons in the conduction band N_{cb} is
+The total number of electrons in the conduction band <math>N_{cb}</math> is
 :<math>N_{cb} = \int_{E_{gap}}^{\infty}N(E) dE = \int_{E_{gap}}^{\infty} \frac{2^{7/2}m^{3/2} \pi}{h^3}(E-E_{gap}^{1/2} \times e^{-\left( E-E_f\right)/kT}dE</math>
@@ Line 142: / Line 142: @@
 :Note: <math>E_{gap}</math> usually makes the exponential term more dominant than the <math>T^{3/2}</math> term.
 [[Forest_Electronic_Instrumentation_and_Measurement]]

@@ Line 135: / Line 135: @@
 ::<math>= frac{2^{5/2}(m\pi kT)^{3/2} }{h^3}e^{-E_{gap}/2kT}</math>
 :: <math>= 4.6 \times 10^{15} \frac{\mbox{electrons}}{\mbox{cm}^3 \mbox{degree K}^{3/2}} T^{3/2}e^{-E_{gap}/2kT}</math>
-:: <math>\propto T^{3/2}</math>
+:: <math>\propto T^{3/2}e^{-E_{gap}/2kT}</math>
 Where
 :<math>E_f \approx E_{gap}/2</math>
 [[Forest_Electronic_Instrumentation_and_Measurement]]

@@ Line 119: / Line 119: @@
-:<math>N(E) dE = \frac{2^{7/2}m^{3/2} \pi}{h^3}(E-E_{gap}^{1/2} \times \frac{1}{e^{\left( E-E_f\right)/kT}+1} dE</math>
+:<math>N(E) dE = \frac{2^{7/2}m^{3/2} \pi}{h^3}(E-E_{gap})^{1/2} \times \frac{1}{e^{\left( E-E_f\right)/kT}+1} dE</math>
 When<math> E</math> is in the conduction band <math>\Rightarrow E-E_f >> kT</math>
@@ Line 134: / Line 134: @@
 :<math>N_{cb} = \int_{E_{gap}}^{\infty}N(E) dE = \int_{E_{gap}}^{\infty} \frac{2^{7/2}m^{3/2} \pi}{h^3}(E-E_{gap}^{1/2} \times e^{-\left( E-E_f\right)/kT}dE</math>
 ::<math>= frac{2^{5/2}(m\pi kT)^{3/2} }{h^3}e^{-E_{gap}/2kT}</math>
-:: <math>= 4.6 \times 10^{15} \frac{\mbox{electrons}}{\mbox{cm}^3 \mbox{degree K}^{-3/2}} T^{3/2}e^{-E_{gap}/2kT}</math>
+:: <math>= 4.6 \times 10^{15} \frac{\mbox{electrons}}{\mbox{cm}^3 \mbox{degree K}^{3/2}} T^{3/2}e^{-E_{gap}/2kT}</math>
 :: <math>\propto T^{3/2}</math>