audio_engineering:class_b_power_calculations
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audio_engineering:class_b_power_calculations [2022/12/13 06:52] – [Power dissipation] mithat | audio_engineering:class_b_power_calculations [2023/08/01 23:47] (current) – [Maximum power dissipation] mithat | ||
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====== Power Calculations for Class B Amplifiers ====== | ====== Power Calculations for Class B Amplifiers ====== | ||
- | The following is derived from material presented by [[https:// | + | For the calculations below, the following are assumed: `v_o` is the amplifier output voltage, `i_o` is the output current, and `R_L` is the load resistance. It's also assumed the amplifier has a bipolar power supply with rails `V_(C C)` and `V_(E E)`, where `V_(E E) = -V_(C C)`. We further assume that transistor base currents are negligible (so collector currents equal output currents) and that the zero-conduction dead zone likewise |
- | + | ||
- | For the calculations below, the following are assumed: `v_o` is the amplifier output voltage, `i_o` is the output current, and `R_L` is the load resistance. It's also assumed the amplifier has a bipolar power supply with rails `V_(C C)` and `V_(E E)`, where `V_(E E) = -V_(C C)`. We further assume that transistor base currents are negligible (so collector currents equal output currents) and that the zero-conduction dead zone is likewise negligible. | + | |
These analyses are based on sinusoidal signals as this is the accepted standard for power and thermal design in audio. The formulae will be valid for other signals with a crest factor of `sqrt(2)`. Alternative analyses based on worst-case signals (i.e., those having a crest factor of one, e.g, square waves), may be instructive but are not presented here. | These analyses are based on sinusoidal signals as this is the accepted standard for power and thermal design in audio. The formulae will be valid for other signals with a crest factor of `sqrt(2)`. Alternative analyses based on worst-case signals (i.e., those having a crest factor of one, e.g, square waves), may be instructive but are not presented here. | ||
+ | A majority of the following is derived from material presented by [[https:// | ||
===== Power into the load ===== | ===== Power into the load ===== | ||
The average output power `bar(P_L)` into load `R_L` for a sine wave with amplitude `v_(op)` is calculated as: | The average output power `bar(P_L)` into load `R_L` for a sine wave with amplitude `v_(op)` is calculated as: | ||
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<WRAP center tip round box 60%> | <WRAP center tip round box 60%> | ||
- | < | + | **Power into the load** |
`bar(P_L) = (v_(op))^2/ | `bar(P_L) = (v_(op))^2/ | ||
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The maximum power into the load happens when `v_(op)` is at its maximum possible value of `V_(C C)`. | The maximum power into the load happens when `v_(op)` is at its maximum possible value of `V_(C C)`. | ||
- | ===== Required supply power ===== | + | ===== Required supply power for given output |
We start by calculating `bar(P_S)_(V+)`, | We start by calculating `bar(P_S)_(V+)`, | ||
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<WRAP center round tip 60%> | <WRAP center round tip 60%> | ||
- | < | + | **Required supply power for given output |
- | `bar(P_S) = 2/pi * v_(op)/R_L * V_(C C)` | + | **`bar(P_S) = 2/pi * v_(op)/R_L * V_(C C)` |
</ | </ | ||
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<WRAP center round tip 60%> | <WRAP center round tip 60%> | ||
- | < | + | **Maximum required supply power** |
`bar(P_S)_max = 2/pi * (V_(C C))^2/R_L` \\ or \\ | `bar(P_S)_max = 2/pi * (V_(C C))^2/R_L` \\ or \\ | ||
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</ | </ | ||
- | ===== Worst-case | + | ===== Maximum |
- | The plot of `P_D` vs. `v_(op)` intersects the origin when `v_(op) = 0` and describes an broad curve with a peak somewhat before its final value (when `v_(op) = V_(C C)`). To find the maxima of this curve, we solve for `(d P_d)/(d v_(op)) = 0`. Thus: | + | The plot of `P_D` vs. `v_(op)` |
`(d P_D)/(d v_(op)) = (2 V_(C C))/(pi R_L) - 2(v_(op)/ | `(d P_D)/(d v_(op)) = (2 V_(C C))/(pi R_L) - 2(v_(op)/ | ||
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`v_(op) = 2/pi V_(C C)` | `v_(op) = 2/pi V_(C C)` | ||
- | Substituting this into the relation for `P_D` above yields the worst-case power dissipation `P_(Dmax)`: | + | Substituting this into the relation for `P_D` above yields the maximum (i.e., |
`P_(Dmax) = ((2 V_(C C))/(pi R_L) * 2/pi V_(C C)) - [(2/pi V_(C C))^2/ | `P_(Dmax) = ((2 V_(C C))/(pi R_L) * 2/pi V_(C C)) - [(2/pi V_(C C))^2/ | ||
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<WRAP center round tip 60%> | <WRAP center round tip 60%> | ||
- | < | + | **Maximum |
`P_(Dmax) = 2/pi^2 * (V_(C C))^2/ | `P_(Dmax) = 2/pi^2 * (V_(C C))^2/ | ||
`P_(Dmax) = 4/pi^2 P_(L max)` | `P_(Dmax) = 4/pi^2 P_(L max)` | ||
- | < | + | **occurs when** |
`v_(op) = 2/pi V_(C C)` | `v_(op) = 2/pi V_(C C)` | ||
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<WRAP center round tip 60%> | <WRAP center round tip 60%> | ||
- | < | + | **Maximum power efficiency** |
`eta_max ~~ 78.5%` | `eta_max ~~ 78.5%` | ||
</ | </ | ||
audio_engineering/class_b_power_calculations.1670914362.txt.gz · Last modified: 2022/12/13 06:52 by mithat