==Forward==
This is a basic guide for some of the common electrical equations used for audio, and why you can't always use them in the simplist form.
In physics, the equations are almost always simple. but the application of the equations is where the complexity lies. In school, great care is taken to use situations where the equations can be used with only minor need for interpretation.
==Units==
This is from basic physics.
Energy -- abilty to do work.
Power -- rate at which work is done.
Voltage -- potential difference (in electric field) that attempts to force electrons to flow.
Current -- flow of electronics.
==Calculus==
small pebbles. most people can easily understand calculus, but often get hung up on some of the algebra used in actual questions.
Limit -- sometimes a function is infinate at some point, eg, (x-1)/(x-1) is not defined for x=1. the limit shows what the value is as x gets very close to 1.
Derivitive -- the rate of change of some function at an instant. basically how fast something is changing right now.
Integral -- the accumulation of something. eg, small pebbels. if you fill an odd shaped object with small pebbles, you can later remove them and place them in a standard, measureable container. the volume is the total volume of the smaller peices that can fill it.
==DC Analysis==
DC stands for "direct current" and is taken to mean "constant". keep in mind that DC voltage doesn't mean DC current, or vice versa. The concept of resistance is brought up here:
Resistance determines the rate at which work is done from a DC circuit, aka the resistance to electrical flow. if little work is done, then resistance is high. Keep in mind this is total work, including work done to generate heat.
Resistance = Voltage / Current
Power = (Voltage) (Current)
==AC Analysis==
AC refers to "alternating current", and is seen as any changing voltage or current. Many systems will have an AC component on top of a DC offset. thus DC and AC can exist in the same system.
in an AC circuit, the shape of the wave is important. The average value of the wave is the "DC offset". the average value is:
DC = (Integral over 1 period of Voltage Wave) / (Period of wave)
Often it is desired to call a wave "fast" and find a "DC equivilent" power output, that way you can say that, after 1 hour, 1kWh has been transfered.
Average Power (aka Watts RMS) = (Integral over 1 period of Power) / (Period of wave)
which breaks down as:
Average Power = Integral over 1 period of (Voltage)(Current) ) / (Period of wave)
==AC and DC with Resistors==
Using the above laws, and assuming resistors, one can see that:
Power = Voltage^2 / Resistance = (Current^2)(Resistance)
And DC-Equivilent voltages or currents can be found using the RMS equation:
RMS Voltage = Square Root of (Average of (Voltage^2))
RMS Current = Square Root of (Average of(Current^2))
For AC the Voltage and Current are rapidly changing, so the question of what value to use comes up. for a SINE wave, there is a known factor of 0.707 that relates the RMS to Peak ration, aka, a 1.414V peak sine wave will have a 1V Rms value. Because we are looking for DC-equivilent, the RMS value is used.
For shorter time scales (eg, if you wanted to determine the power use for short periods of time), the integral for RMS (voltage or current) or Average (for power) can be used with the length of the "Period" changed.
==Energy Storage==
To this point, we've only looked at devices that use power. but some devices STORE energy (which takes power to transfer), and can later release this energy back.
Capacitance, this referes to the ability of a device to store energy in an electric field.
Current = (Capacitance)(Rate of change of voltage across device)
Energy in Cap = 0.5 Capacitance (Voltage^2)
Inductance, refers to the ability of a device to store energy in a magnetic field.
Voltage = (Inductance)(Rate of change of current through device)
Energy in Inductor = 0.5 Inductance (Current^2)
==Phase==
One neat thing about sine waves is that the derivitive and integral are also sine waves, just different in phase. eg, the sine wave will look like either cosine or -cosine.
Revisting RMS:
the RMS or Average equations involved integrating power, which is the product of voltage and current. but with voltage and current not in phase, there will be periods of positive power transfer and periods of negative power transfer. this makes sense as capacitors and inductors can't do any work, so the net power transfer (for AC) must be 0.
==Complex Power==
As shown above, the power to the device is based upon the voltage and current, and how well they line up. It can be shown that, for AC:
Real Power = (RMS Voltage)(RMS Current)(Power Factor)
where Power Factor is between 0 and 1 (for devices that cannot generate power on their own).
==Conclusions==
Because Average Power is not RMS Voltage * RMS Current, but rather Average (Voltage * Current), a false high reading can be had if you measure just RMS voltage and/or RMS currents. for this reason, the DMM and Clamp will not give you an indication of how much real power is transfered, nor will it tell you how much resistance/inductance/capacitance there is. The DMM + Clamp will show you only the magnitude of the impedance (combined resistance and reactance).
Someone asked why i don't post more tech threads, so i figured i'd try it out. Any questions over this. i tired to make it breif and understandable, but I know that often means it only makes sense if you already know it.
I've attempted to not use the * for multiplication, as the symbol has other meanings in (slightly) more advanced analysis.
edit--
Corrected the offhand use of "RMS Power" to the more correct "Average Power". RMS is a math tool to show "DC equivilent" voltages and currents, but a "DC equivilent" power would be an average of power.
This is a basic guide for some of the common electrical equations used for audio, and why you can't always use them in the simplist form.
In physics, the equations are almost always simple. but the application of the equations is where the complexity lies. In school, great care is taken to use situations where the equations can be used with only minor need for interpretation.
==Units==
This is from basic physics.
Energy -- abilty to do work.
Power -- rate at which work is done.
Voltage -- potential difference (in electric field) that attempts to force electrons to flow.
Current -- flow of electronics.
==Calculus==
small pebbles. most people can easily understand calculus, but often get hung up on some of the algebra used in actual questions.
Limit -- sometimes a function is infinate at some point, eg, (x-1)/(x-1) is not defined for x=1. the limit shows what the value is as x gets very close to 1.
Derivitive -- the rate of change of some function at an instant. basically how fast something is changing right now.
Integral -- the accumulation of something. eg, small pebbels. if you fill an odd shaped object with small pebbles, you can later remove them and place them in a standard, measureable container. the volume is the total volume of the smaller peices that can fill it.
==DC Analysis==
DC stands for "direct current" and is taken to mean "constant". keep in mind that DC voltage doesn't mean DC current, or vice versa. The concept of resistance is brought up here:
Resistance determines the rate at which work is done from a DC circuit, aka the resistance to electrical flow. if little work is done, then resistance is high. Keep in mind this is total work, including work done to generate heat.
Resistance = Voltage / Current
Power = (Voltage) (Current)
==AC Analysis==
AC refers to "alternating current", and is seen as any changing voltage or current. Many systems will have an AC component on top of a DC offset. thus DC and AC can exist in the same system.
in an AC circuit, the shape of the wave is important. The average value of the wave is the "DC offset". the average value is:
DC = (Integral over 1 period of Voltage Wave) / (Period of wave)
Often it is desired to call a wave "fast" and find a "DC equivilent" power output, that way you can say that, after 1 hour, 1kWh has been transfered.
Average Power (aka Watts RMS) = (Integral over 1 period of Power) / (Period of wave)
which breaks down as:
Average Power = Integral over 1 period of (Voltage)(Current) ) / (Period of wave)
==AC and DC with Resistors==
Using the above laws, and assuming resistors, one can see that:
Power = Voltage^2 / Resistance = (Current^2)(Resistance)
And DC-Equivilent voltages or currents can be found using the RMS equation:
RMS Voltage = Square Root of (Average of (Voltage^2))
RMS Current = Square Root of (Average of(Current^2))
For AC the Voltage and Current are rapidly changing, so the question of what value to use comes up. for a SINE wave, there is a known factor of 0.707 that relates the RMS to Peak ration, aka, a 1.414V peak sine wave will have a 1V Rms value. Because we are looking for DC-equivilent, the RMS value is used.
For shorter time scales (eg, if you wanted to determine the power use for short periods of time), the integral for RMS (voltage or current) or Average (for power) can be used with the length of the "Period" changed.
==Energy Storage==
To this point, we've only looked at devices that use power. but some devices STORE energy (which takes power to transfer), and can later release this energy back.
Capacitance, this referes to the ability of a device to store energy in an electric field.
Current = (Capacitance)(Rate of change of voltage across device)
Energy in Cap = 0.5 Capacitance (Voltage^2)
Inductance, refers to the ability of a device to store energy in a magnetic field.
Voltage = (Inductance)(Rate of change of current through device)
Energy in Inductor = 0.5 Inductance (Current^2)
==Phase==
One neat thing about sine waves is that the derivitive and integral are also sine waves, just different in phase. eg, the sine wave will look like either cosine or -cosine.
Revisting RMS:
the RMS or Average equations involved integrating power, which is the product of voltage and current. but with voltage and current not in phase, there will be periods of positive power transfer and periods of negative power transfer. this makes sense as capacitors and inductors can't do any work, so the net power transfer (for AC) must be 0.
==Complex Power==
As shown above, the power to the device is based upon the voltage and current, and how well they line up. It can be shown that, for AC:
Real Power = (RMS Voltage)(RMS Current)(Power Factor)
where Power Factor is between 0 and 1 (for devices that cannot generate power on their own).
==Conclusions==
Because Average Power is not RMS Voltage * RMS Current, but rather Average (Voltage * Current), a false high reading can be had if you measure just RMS voltage and/or RMS currents. for this reason, the DMM and Clamp will not give you an indication of how much real power is transfered, nor will it tell you how much resistance/inductance/capacitance there is. The DMM + Clamp will show you only the magnitude of the impedance (combined resistance and reactance).
Someone asked why i don't post more tech threads, so i figured i'd try it out. Any questions over this. i tired to make it breif and understandable, but I know that often means it only makes sense if you already know it.
I've attempted to not use the * for multiplication, as the symbol has other meanings in (slightly) more advanced analysis.
edit--
Corrected the offhand use of "RMS Power" to the more correct "Average Power". RMS is a math tool to show "DC equivilent" voltages and currents, but a "DC equivilent" power would be an average of power.
