Passive Filters - Revision history

Hwang: /* Low-Pass Filters (LPF) */

2006-07-06T21:45:01Z

Low-Pass Filters (LPF)

← Older revision		Revision as of 16:45, 6 July 2006
Line 17:		Line 17:
	Here are plots comparing the input and output voltages for two different frequencies:		Here are plots comparing the input and output voltages for two different frequencies:

	[[Image:~~RC_LPC_freq_compare~~.gif]]		[[Image:RC_LPF_freq_compare.gif]]

	As we can see, the filter blocks the higher frequencies.		As we can see, the filter blocks the higher frequencies.

Hwang: /* High-Pass Filter (HPF) */

2006-07-06T21:44:23Z

High-Pass Filter (HPF)

← Older revision		Revision as of 16:44, 6 July 2006
Line 38:		Line 38:
	Here are some plots comparing the input and output voltages for two different frequencies:		Here are some plots comparing the input and output voltages for two different frequencies:

	[[Image:~~RC_HPF_freq_response~~.gif]]		[[Image:RC_HPF_freq_compare.gif]]

	This time, the filter blocks the lower frequencies.		This time, the filter blocks the lower frequencies.

Hwang: /* High-Pass Filter (HPF) */

2006-07-06T21:43:18Z

High-Pass Filter (HPF)

← Older revision		Revision as of 16:43, 6 July 2006
Line 35:		Line 35:

	[[Image:RC_HPF_magnitude_Response.gif]]		[[Image:RC_HPF_magnitude_Response.gif]]

			Here are some plots comparing the input and output voltages for two different frequencies:

			[[Image:RC_HPF_freq_response.gif]]

	This time, the filter blocks the lower frequencies.		This time, the filter blocks the lower frequencies.

Hwang: /* Low-Pass Filters (LPF) */

2006-07-06T21:42:28Z

Low-Pass Filters (LPF)

← Older revision		Revision as of 16:42, 6 July 2006
Line 14:		Line 14:

	[[Image:RC_LPF_magnitude_response.gif]]		[[Image:RC_LPF_magnitude_response.gif]]

			Here are plots comparing the input and output voltages for two different frequencies:

			[[Image:RC_LPC_freq_compare.gif]]

	As we can see, the filter blocks the higher frequencies.		As we can see, the filter blocks the higher frequencies.

Hwang at 20:24, 6 July 2006

2006-07-06T20:24:25Z

← Older revision		Revision as of 15:24, 6 July 2006
Line 13:		Line 13:
	When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at <math>V_out</math> depends on the frequency of our source. Here is a plot of the magnitude response of the filter, on a logarithmic scale from 10Hz to 10MHz:		When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at <math>V_out</math> depends on the frequency of our source. Here is a plot of the magnitude response of the filter, on a logarithmic scale from 10Hz to 10MHz:

	[[Image:~~RC_LPF_frequncy_response~~.gif]]		[[Image:RC_LPF_magnitude_response.gif]]

	As we can see, the filter blocks the higher frequencies.		As we can see, the filter blocks the higher frequencies.
Line 30:		Line 30:
	The magnitude response of a filter with R=500Ω and C=2nF looks like this:		The magnitude response of a filter with R=500Ω and C=2nF looks like this:

	[[Image:~~RC_HPF_frequency_Response~~.gif]]		[[Image:RC_HPF_magnitude_Response.gif]]

	This time, the filter blocks the lower frequencies.		This time, the filter blocks the lower frequencies.

Hwang at 20:23, 6 July 2006

2006-07-06T20:23:15Z

← Older revision		Revision as of 15:23, 6 July 2006
Line 11:		Line 11:
	[[Image:RC_LPF_schematic.gif]]		[[Image:RC_LPF_schematic.gif]]

	When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at <math>V_out</math> depends on the frequency of our source. Here is a plot of the ~~frequency~~ response of the filter, on a logarithmic scale from 10Hz to 10MHz:		When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at <math>V_out</math> depends on the frequency of our source. Here is a plot of the magnitude response of the filter, on a logarithmic scale from 10Hz to 10MHz:

	[[Image:RC_LPF_frequncy_response.gif]]		[[Image:RC_LPF_frequncy_response.gif]]
Line 28:		Line 28:
	[[Image:RC_HPF_schematic.gif]]		[[Image:RC_HPF_schematic.gif]]

	The ~~frequncy~~ response of a filter with R=500Ω and C=2nF looks like this:		The magnitude response of a filter with R=500Ω and C=2nF looks like this:

	[[Image:RC_HPF_frequency_Response.gif]]		[[Image:RC_HPF_frequency_Response.gif]]

Hwang at 20:21, 6 July 2006

2006-07-06T20:21:55Z

← Older revision		Revision as of 15:21, 6 July 2006
Line 1:		Line 1:
	__TOC__		__TOC__
	We can build some very simple filters out of a capacitor and a resistor. A filter ~~will block~~ some frequencies, while admitting others.		We can build some very simple filters out of a capacitor and a resistor. A filter blocks some frequencies, while admitting others.

	Better filters can be made out of op-amps.		Better filters can be made out of op-amps.

	==Low-Pass Filters (LPF)==		==Low-Pass Filters (LPF)==
	A low pass filter ~~will admit~~ lower frequencies and ~~block~~ out high ones. This can help us smooth out our signals and get rid of high frequency noise.		A low-pass filter admits lower frequencies and blocks out high ones. This can help us smooth out our signals and get rid of high frequency noise.

	We can make one by hooking up our capacitor and resistor like this:		We can make one by hooking up our capacitor and resistor like this:
Line 15:		Line 15:
	[[Image:RC_LPF_frequncy_response.gif]]		[[Image:RC_LPF_frequncy_response.gif]]

	As we can see, the filter blocks the higher ~~frequncies~~.		As we can see, the filter blocks the higher frequencies.

	~~Since a~~ square wave is made out of a superposition of many sine waves, the low-pass filter ~~will~~ ~~block~~ the sine waves with higher frequencies. Our input and output ~~will look~~ like:		A square wave is made out of a superposition of many sine waves, the low-pass filter blocks out the sine waves with higher frequencies. Our input and output looks like:

	[[Image:RC_LPF_square_wave.gif]](C=200uF, R=500Ω)		[[Image:RC_LPF_square_wave.gif]](C=200uF, R=500Ω)

	==High-Pass Filter (HPF)==		==High-Pass Filter (HPF)==
	A high pass filter ~~will block~~ out lower frequencies while letting high frequencies through. The output ~~will~~ ~~respond~~ more strongly to changes in the input signal, such as that coming from a motion detector.		A high-pass filter blocks out lower frequencies while letting high frequencies through. The output signal responds more strongly to changes in the input signal, such as that coming from a motion detector.

	We can make a simple high-pass filter by hooking up our capacitor and resistor like this:		We can make a simple high-pass filter by hooking up our capacitor and resistor like this:

Hwang at 16:30, 5 July 2006

2006-07-05T16:30:11Z

← Older revision		Revision as of 11:30, 5 July 2006
Line 39:		Line 39:

	Notice that when the input voltage drops to zero, the output voltage becomes negative. This is because the capacitor is discharging, and forcing the current backwards.		Notice that when the input voltage drops to zero, the output voltage becomes negative. This is because the capacitor is discharging, and forcing the current backwards.

			==References==
			Hayt, William H. Jr., Jack E. Kemmerly, and Steven M. Durbin. <u>Engineering Circuit Analysis</u>. 6th ed. New York:McGraw-Hill, 2002.

Hwang at 22:08, 20 June 2006

2006-06-20T22:08:18Z

← Older revision		Revision as of 17:08, 20 June 2006
Line 1:		Line 1:
			__TOC__
	==RL Circuits==
			We can build some very simple filters out of a capacitor and a resistor. A filter will block some frequencies, while admitting others.
	===Charging===
	If the inductor is initially uncharged and we want to charge it by inserting a voltage source <math>V_s</math> in the RL circuit:

			Better filters can be made out of op-amps.
⚫	[[Image:~~RL_charge_schematic~~.gif]]

			==Low-Pass Filters (LPF)==
	The inductor initially has a very high resistance, as energy is going into building up a magnetic field. Once the magnetic field is up and no longer changing, the inductor will act like a short circuit. The current at steady state will be equal to <math>I_0=V_s/R</math>. Since the inductor is acting like a short circuit at steady state, the voltage across the inductor then will be 0. The current through the inductor is given by:
			A low pass filter will admit lower frequencies and block out high ones. This can help us smooth out our signals and get rid of high frequency noise.

			We can make one by hooking up our capacitor and resistor like this:
	<math>i_L(t)=I_0(1-e^{-\frac{R}{L}t})</math>

		⚫	[[Image:RC_LPF_schematic.gif]]

			When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at <math>V_out</math> depends on the frequency of our source. Here is a plot of the frequency response of the filter, on a logarithmic scale from 10Hz to 10MHz:
	===Discharging===
	In the following circuit, the inductor initially has current <math>I_0=V_s/R</math> flowing through it; we replace the voltage source with a short circuit at <math>t=0</math>.

	[[Image:~~RL_discharge_schematic~~.gif]]		[[Image:RC_LPF_frequncy_response.gif]]

			As we can see, the filter blocks the higher frequncies.
	After we cut out the voltage source, the voltage across the inductor will be <math>I_0*R</math>, but the higher voltage will be at the negative terminal of the inductor. Thus, <math>I_0=-V/R</math>. The the current flowing through the inductor at time ''t'' is given by:

			Since a square wave is made out of a superposition of many sine waves, the low-pass filter will block the sine waves with higher frequencies. Our input and output will look like:
	<math>i_L(t)=I_0e^{-\frac{R}{L}t}</math>

			[[Image:RC_LPF_square_wave.gif]](C=200uF, R=500Ω)
	where <math>I_0=-V_s/R</math>.

			==High-Pass Filter (HPF)==
	The ''time constant'' for the RL circuit is equal to <math>L/R</math>.
			A high pass filter will block out lower frequencies while letting high frequencies through. The output will respond more strongly to changes in the input signal, such as that coming from a motion detector.

			We can make a simple high-pass filter by hooking up our capacitor and resistor like this:
	The voltage and current of the inductor for the circuits above are given by the graphs below, from ''t=0'' to ''t=5L/R''. The voltage is measured at the "+" terminal of the inductor, relative to the ground. A positive current flows into the inductor from this terminal; a negative current flows out of this terminal.:

			[[Image:RC_HPF_schematic.gif]]
	{\| border="1" cellspacing="0" cellpadding="5" align="center"
	\|+'''Inductor'''
	\|-
	! !!Voltage !! Current
	\|-
	!Charge !! [[Image:RL_charge_voltage.gif]] \|\| [[Image:RL_charge_current.gif]]
	\|-
	!Discharge !! [[Image:RL_discharge_voltage.gif]] \|\| [[Image:RL_discharge_current.gif]]
	\|-
	\|}

			The frequncy response of a filter with R=500Ω and C=2nF looks like this:
	Remember that for an inductor, <math>v(t)=L*di/dt</math>. Note that the voltage across the inductor can change instantly at ''t=0'', but the current changes slowly.

			[[Image:RC_HPF_frequency_Response.gif]]

			This time, the filter blocks the lower frequencies.

			When we put a square wave though the filter, the resulting waveform looks like this:

			[[Image:RC_HPF_square_wave.gif]](C=200uF, R=500Ω)

			Notice that when the input voltage drops to zero, the output voltage becomes negative. This is because the capacitor is discharging, and forcing the current backwards.

Hwang at 22:07, 20 June 2006

2006-06-20T22:07:12Z

← Older revision		Revision as of 17:07, 20 June 2006
Line 1:		Line 1:
			==RL Circuits==
	__TOC__
			===Charging===
	We can build some very simple filters out of a capacitor and a resistor. A filter will block some frequencies, while admitting others.
			If the inductor is initially uncharged and we want to charge it by inserting a voltage source <math>V_s</math> in the RL circuit:

			[[Image:RL_charge_schematic.gif]]
	Better filters can be made out of op-amps.

			The inductor initially has a very high resistance, as energy is going into building up a magnetic field. Once the magnetic field is up and no longer changing, the inductor will act like a short circuit. The current at steady state will be equal to <math>I_0=V_s/R</math>. Since the inductor is acting like a short circuit at steady state, the voltage across the inductor then will be 0. The current through the inductor is given by:
	==Low-Pass Filters (LPF)==
	A low pass filter will admit lower frequencies and block out high ones. This can help us smooth out our signals and get rid of high frequency noise.

			<math>i_L(t)=I_0(1-e^{-\frac{R}{L}t})</math>
	We can make one by hooking up our capacitor and resistor like this:

	[[Image:RC_LPF_schematic.jpg]]

			===Discharging===
	When set R=500Ω and C=2nF, and hook up an AC voltage source, the voltage we see at <math>V_out</math> depends on the frequency of our source. Here is a plot of the frequency response of the filter, on a logarithmic scale from 10Hz to 10MHz:
			In the following circuit, the inductor initially has current <math>I_0=V_s/R</math> flowing through it; we replace the voltage source with a short circuit at <math>t=0</math>.

	[[Image:~~RC_LPF_frequncy_response~~.~~jpg~~]]		[[Image:RL_discharge_schematic.gif]]

			After we cut out the voltage source, the voltage across the inductor will be <math>I_0*R</math>, but the higher voltage will be at the negative terminal of the inductor. Thus, <math>I_0=-V/R</math>. The the current flowing through the inductor at time ''t'' is given by:
	As we can see, the filter blocks the higher frequncies.

			<math>i_L(t)=I_0e^{-\frac{R}{L}t}</math>
	Since a square wave is made out of a superposition of many sine waves, the low-pass filter will block the sine waves with higher frequencies. Our input and output will look like:

			where <math>I_0=-V_s/R</math>.
	[[Image:RC_LPF_square_wave.jpg]](C=200uF, R=500Ω)

			The ''time constant'' for the RL circuit is equal to <math>L/R</math>.
	==High-Pass Filter (HPF)==
	A high pass filter will block out lower frequencies while letting high frequencies through. The output will respond more strongly to changes in the input signal, such as that coming from a motion detector.

			The voltage and current of the inductor for the circuits above are given by the graphs below, from ''t=0'' to ''t=5L/R''. The voltage is measured at the "+" terminal of the inductor, relative to the ground. A positive current flows into the inductor from this terminal; a negative current flows out of this terminal.:
	We can make a simple high-pass filter by hooking up our capacitor and resistor like this:

			{\| border="1" cellspacing="0" cellpadding="5" align="center"
	[[Image:RC_HPF_schematic.jpg]]
			\|+'''Inductor'''
			\|-
			! !!Voltage !! Current
			\|-
			!Charge !! [[Image:RL_charge_voltage.gif]] \|\| [[Image:RL_charge_current.gif]]
			\|-
			!Discharge !! [[Image:RL_discharge_voltage.gif]] \|\| [[Image:RL_discharge_current.gif]]
			\|-
			\|}

			Remember that for an inductor, <math>v(t)=L*di/dt</math>. Note that the voltage across the inductor can change instantly at ''t=0'', but the current changes slowly.
	The frequncy response of a filter with R=500Ω and C=2nF looks like this:

	[[Image:RC_HPF_frequency_Response.jpg]]

	This time, the filter blocks the lower frequencies.

	When we put a square wave though the filter, the resulting waveform looks like this:

	[[Image:RC_HPF_square_wave.jpg]](C=200uF, R=500Ω)

	Notice that when the input voltage drops to zero, the output voltage becomes negative. This is because the capacitor is discharging, and forcing the current backwards.