TF EIM Chapt9 - Revision history

Foretony: /* Op Amp Noise */

2011-04-20T16:45:28Z

Op Amp Noise

2011-04-20T16:43:29Z

Input Offset Voltage

2011-04-20T16:10:41Z

Input Offset Voltage

2011-04-20T07:20:05Z

Slew Rates

2011-04-20T07:09:47Z

Op Amp Noise

2011-04-20T07:00:26Z

Op Amp Noise

2011-04-20T06:57:19Z

Op Amp Noise

2011-04-20T06:38:41Z

Vout

2011-04-17T03:20:10Z

input bias offset current

2011-04-17T03:18:48Z

NonZero input bias current I_B

@@ Line 276: / Line 276: @@
 So the total noise of the amplifier is given as
-:<math>V_{ntot} = \sqrt{V_n^2 + V_{ni}^2} + V_{ns}^2}</math>
+:<math>V_{ntot} = \sqrt{V_n^2 + V_{ni}^2 + V_{ns}^2}</math>
 This noise gets amplified by the Op Amp and modulated by the Band width such that
-<math>V_{no} = V_{ntot} Gain \sqrt{B_W} = \sqrt{V_n^2 + V_{ni}^2} + V_{ns}^2} Gain \sqrt{B_W}</math>
+<math>V_{no} = V_{ntot} Gain \sqrt{B_W} = \sqrt{V_n^2 + V_{ni}^2 + V_{ns}^2} Gain \sqrt{B_W}</math>
 [[Forest_Electronic_Instrumentation_and_Measurement]]

@@ Line 176: / Line 176: @@
 <math>V_{out} -I_(R_1+R_2) =0 \Rightarrow I = \frac{V_{out}}{R_1 + R_2}</math>
-<math>V_{io} - I R_1= 0 \Rightarrow V_{out} = I R_1 = \frac{V_{out}}{R_1 + R_2} R_1</math>
+<math>V_{io} - I R_1= 0 \Rightarrow V_{io} = I R_1 = \frac{V_{out}}{R_1 + R_2} R_1</math>
 : <math>V_{out} = \frac{R_2}{R_1+R_2} V_{io} = \left ( 1 + \frac{R_2}{R_1} \right ) V_{io}</math>

@@ Line 176: / Line 176: @@
 <math>V_{out} -I_(R_1+R_2) =0 \Rightarrow I = \frac{V_{out}}{R_1 + R_2}</math>
-<math>V_{io} - I_R1= 0 \Rightarrow V_{out} = I R_1 = \frac{V_{out}}{R_1 + R_2} R_1</math>
+<math>V_{io} - I R_1= 0 \Rightarrow V_{out} = I R_1 = \frac{V_{out}}{R_1 + R_2} R_1</math>
 : <math>V_{out} = \frac{R_2}{R_1+R_2} V_{io} = \left ( 1 + \frac{R_2}{R_1} \right ) V_{io}</math>
 : A direct measurement of <math>V_{io}</math> can be made if you set <math>R_2</math> to give you a large gain and have <math>V_{in}</math> = 0 (no input).  What you measure at <math>V_{out}</math> will be <math>V_{io}</math>.
 ===Vout===

← Older revision		Revision as of 07:20, 20 April 2011
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	==Slew Rates==		==Slew Rates==

		+	The Slew Rate is defined as the maximum rate at which the Op AMp voltage can change.
		+
		+	This can be observed as an increase in the rise time of an input pulse (a Capacitive effect).
		+
		+	If the AC input to an Op Amp is a square wave then as the frequency increases you will start to see the square wave input become rounded.
		+
		+	The Slew rate is the voltage swing divided by the amount of time needed to make that swing (ie the slope of the Voltage -vs- time plot).
		+
		+
		+	You can then calculate the mximum input frequency which will be free of distortion using this Slew Rate
		+
		+	: <math>\nu = \frac{Slew Rate}{2 \pi \Delta V}</math>
		+
		+	Where <math>\Delta V</math> = peak -to - peak voltage swing of your input signal.
		+
		+
		+	How do you get the above?
		+
		+	Assum your input signal is a cosine wave and take the derivative to get the slew rate
		+
		+	Slew Rate <math>\equiv \left ( \frac{V}{t} \right )_{max} = \left . \omega V_0 \cos (\omega t) \right \|_{max} = 2 \pi \nu V_0</math>

	==PSRR (Power Supply Rejection Ratio==		==PSRR (Power Supply Rejection Ratio==

← Older revision		Revision as of 07:09, 20 April 2011
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	<math>\Rightarrow</math> Resistor Noise = <math>\sqrt{4kTR} = \frac{V_{ns}}{\sqrt{B_W}} = Volts / sqrt{Hz}</math>		<math>\Rightarrow</math> Resistor Noise = <math>\sqrt{4kTR} = \frac{V_{ns}}{\sqrt{B_W}} = Volts / sqrt{Hz}</math>
		+
		+
		+	Another source of Noise is the noise from the source driving the Op Amp
		+	:<math>V_{ns} \equiv</math> noise instrinsic to the source driving the Op Amp
		+
		+	The third source of noise is the current which traverses the two Op Amp inputs through the internal resistance of the Op Amp (R_{in}).
		+
		+	:V_{ni} = i_n R_{in} = internal noise of the amplifier
		+
		+	So the total noise of the amplifier is given as
		+
		+	:<math>V_{ntot} = \sqrt{V_n^2 + V_{ni}^2} + V_{ns}^2}</math>
		+
		+	This noise gets amplified by the Op Amp and modulated by the Band width such that
		+
		+	<math>V_{no} = V_{ntot} Gain \sqrt{B_W} = \sqrt{V_n^2 + V_{ni}^2} + V_{ns}^2} Gain \sqrt{B_W}</math>
		+

	[[Forest_Electronic_Instrumentation_and_Measurement]]		[[Forest_Electronic_Instrumentation_and_Measurement]]

@@ Line 242: / Line 242: @@
 So the RMS noise is given as
-:<math>\sqrt{\bar{V_n^2}} = \sqrt{4kTRB_w}</math>
+:<math>V_{ns} \equiv \sqrt{\bar{V_n^2}} = \sqrt{4kTRB_w}</math>= noise voltage
 [[Forest_Electronic_Instrumentation_and_Measurement]]

← Older revision		Revision as of 06:57, 20 April 2011
Line 221:		Line 221:
	==Op Amp Noise==		==Op Amp Noise==

		+
		+	The noise that an Op Amp produces at its output is dependent on the noise that is injected by its input and the Gain of the Op Amp.
		+
		+	In the inverting Op Amp circuit you have 2 resistors which determine the Gain. Resistors have an intrinsic noise, called Johnson noise, which is due to their temperature. Electrons traversing the resistor, although they are being directed by an electric field, will have thermal energy that results in a fluctuation in the voltage difference across the ends of the resistor.
		+
		+	J.B. Johnson found that the square of the noise voltage varies linearly with the resistance. He also showed that the power associated with the fluctuations varied linearly with the bandwidth of the measuring instrument. Or in General
		+
		+	:<math>\bar{V_n^2} = 4kTRB_w</math>
		+
		+	where
		+
		+	<math>V_n</math> = the noise voltage
		+
		+	<math>B_W</math> = bandwidth of measuring insturment
		+
		+	k = Boltzman's contant
		+
		+	T=Temperature
		+
		+	So the RMS noise is given as
		+
		+	:<math>\sqrt{\bar{V_n^2}} = \sqrt{4kTRB_w}</math>

	[[Forest_Electronic_Instrumentation_and_Measurement]]		[[Forest_Electronic_Instrumentation_and_Measurement]]

← Older revision		Revision as of 06:38, 20 April 2011
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	; V_{io} can be either > 0 or < 0.		; V_{io} can be either > 0 or < 0.
		+
		+	==Slew Rates==
		+
		+
		+	==PSRR (Power Supply Rejection Ratio==
		+
		+
		+	The ripple of a DC power supply to an Op Amp can produce a ripple on the Op Amp output.
		+
		+	This is because changes in the power supply voltage result in changes in the input offset voltage (V_{io})
		+
		+
		+	The output voltage from the inverting and non-inverting Op AMp is given by
		+
		+	:<math>V_{out} = \left ( 1 + \frac{R_2}{R_1}\right ) V_{io}</math>
		+
		+	:<math>\Rightarrow \Delta V_{out} = \left ( 1 + \frac{R_2}{R_1}\right ) \Delta V_{io}</math>
		+	:: <math>= \left ( 1 + \frac{R_2}{R_1}\right ) \left ( PSRR \Delta V_{cc} \right )</math>
		+
		+	where
		+
		+	:<math>PSSR \equiv \frac{\Delta V_{io}}{\Delta V_{cc}}</math>
		+
		+
		+	To measure PSRR you set<math> V_{in}</math> to zero (no input) then measure <math>V_{out}</math> for several <math>V_{cc}</math>.
		+
		+	A plot of <math>\Delta V_{out} -vs \Delta V_{cc}</math> will have a slope that relates to PSSR.
		+
		+	==Op Amp Noise==
		+

	[[Forest_Electronic_Instrumentation_and_Measurement]]		[[Forest_Electronic_Instrumentation_and_Measurement]]

← Older revision		Revision as of 03:20, 17 April 2011
Line 126:		Line 126:


−	You can do this by using the other half of the amplifier, the non-inverting input current I_{B2}.	+	You can do this by using the other half of the amplifier, the non-inverting input current <math>I_{B2}</math>.

	If you use a pull up resister (<math>R_3)</math> to raise the non-inverting input from ground then there will be a potential difference created from the current <math>I_{B2}</math>		If you use a pull up resister (<math>R_3)</math> to raise the non-inverting input from ground then there will be a potential difference created from the current <math>I_{B2}</math>

← Older revision		Revision as of 03:18, 17 April 2011
Line 117:		Line 117:


−	~~Iff~~ V_{in} >> I_{B1}R_2 then your Op Amp will operate close to a perfect one.	+	If <math>V_{in} >> I_{B1}R_2</math> then your Op Amp will operate close to a perfect one.

	===input bias offset current===		===input bias offset current===