Hi All,
Recently I've come upon a result which, while inherent in the theory of electricity, has not been noticed so far. Lately, I found a great way to demonstrate it using PSpice which eliminates the need for expensive equipment and/or tedious calculations.
Create a schematic in PSpice (cf. the attachment) of an RC circuit powered by an 800kHz pulse generator, voltage amplitude of 1.17V and a voltage offset of -3.356V. The value of R is 9.9244Ohms and the value of C is 115pF. Run the simulation from 1.25ms to 2.5ms at 1.25ns increment (that's one period). Once the simulation completes transfer the data into an Excel spreadsheet (by going to Edit->Select All->Copy).
Then calculate the input power Ein as the average of the instantaneous products Ii*Vi of the instantaneous current Ii and voltage Vi values. Do the same for the output power Pout where you would average over the instantaneous values of the product Ii*Ii*R. Then form the quotient Pot/Pin and you will see an amazing thing. Not only Pout differs from Pin but Pin has negative value. Negative value of Pin means that all the power is returned to the power source. Thus, not only is Joule heat produced in the dissipative element, active R, but, in addition, energy is returned to the source. A similar effect can be observed with an LRC circuit with properly chosen values of the elements. In the LRC circuit the Pout/Pin > 1 effect can be achieved even in absence of voltage offset.
One warning. Don't use the power analysis, part of SPice because it is based on procedures involving many more arithmetic operations than the procedure I described which leads to inevitable amassing of errors due to the essence of the digital machine we're using for this calculation. These errors will obscure the above effect.
The procedure I described is the most transparent and straightforward possible procedure of processing exact data such as the list of Ii's and Vi's produced by the simulation. You may want to note that the product Ii*Vi is the value of the instantaneous slope of the energy-time curve. The sum of all the Ii*Vi products, divided by the number of points n will give the average power Pin over the entire period. Therefore, we don't need integration or any other procedure, especially containing approximations, to determine what the average power during the period is. The same applies for Pout, when averaging over all Ii*Ii*R values within that period.
Those interested in discussing this phenomenon in more detail or for some other reason may also sign up at actascientiae.org/v. That board is also LaTeX enhanced.
Recently I've come upon a result which, while inherent in the theory of electricity, has not been noticed so far. Lately, I found a great way to demonstrate it using PSpice which eliminates the need for expensive equipment and/or tedious calculations.
Create a schematic in PSpice (cf. the attachment) of an RC circuit powered by an 800kHz pulse generator, voltage amplitude of 1.17V and a voltage offset of -3.356V. The value of R is 9.9244Ohms and the value of C is 115pF. Run the simulation from 1.25ms to 2.5ms at 1.25ns increment (that's one period). Once the simulation completes transfer the data into an Excel spreadsheet (by going to Edit->Select All->Copy).
Then calculate the input power Ein as the average of the instantaneous products Ii*Vi of the instantaneous current Ii and voltage Vi values. Do the same for the output power Pout where you would average over the instantaneous values of the product Ii*Ii*R. Then form the quotient Pot/Pin and you will see an amazing thing. Not only Pout differs from Pin but Pin has negative value. Negative value of Pin means that all the power is returned to the power source. Thus, not only is Joule heat produced in the dissipative element, active R, but, in addition, energy is returned to the source. A similar effect can be observed with an LRC circuit with properly chosen values of the elements. In the LRC circuit the Pout/Pin > 1 effect can be achieved even in absence of voltage offset.
One warning. Don't use the power analysis, part of SPice because it is based on procedures involving many more arithmetic operations than the procedure I described which leads to inevitable amassing of errors due to the essence of the digital machine we're using for this calculation. These errors will obscure the above effect.
The procedure I described is the most transparent and straightforward possible procedure of processing exact data such as the list of Ii's and Vi's produced by the simulation. You may want to note that the product Ii*Vi is the value of the instantaneous slope of the energy-time curve. The sum of all the Ii*Vi products, divided by the number of points n will give the average power Pin over the entire period. Therefore, we don't need integration or any other procedure, especially containing approximations, to determine what the average power during the period is. The same applies for Pout, when averaging over all Ii*Ii*R values within that period.
Those interested in discussing this phenomenon in more detail or for some other reason may also sign up at actascientiae.org/v. That board is also LaTeX enhanced.
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