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--- other:electronics:rectifier-circuit [2024/06/04 15:01] – [Basic Equations] oscar
+++ other:electronics:rectifier-circuit [2024/06/14 12:34] (current) – [Transformer Selection] oscar
@@ Line 19: / Line 19: @@
 {{ :other:electronics:wave-measurements.jpg?400 |}}
-Some relevant basic equations are:
+These values can be easily converted to each other. The way formulas for these conversions differ upon the the waveform that applies (sinus, triangle, square). The relevant basic conversions are:
-RMS (root mean square) and PP (peak-to-peak) values can be converted with the following formulas : \\
+==== Sinus ====
-For voltages: \\
+  * ''** V//p// = V//pp// / 2 **''
+  * ''** V//dc// = V//avg// = ( 2 * V//p// ) / π  **''
+  * ''** V//rms// = V//p// / √(2) **''
+  * ''** V//rms// = V//pp// / (2 * √(2)) **''
+  * ''** V//pp// = 2*√(2) * V//rms// **''
-''** V//dc// = V//avg// = ( 2 * V//peak// ) / π  **''
+==== Triangle ====
+  * ''** V//dc// = V//avg// = V//p// / 2  **''
-''**
+  * ''** V//rms// = V//p// / √(3) **''
-V//pp// = √(2) * V//rms// \\
-\\
+==== Square ====
-V//rms// = V//pp// / √(2) \\
+  * ''** V//p// = V//pp// / 2 **''
-**''
+  * ''** V//dc// = V//avg// = V//p//  **''
-\\
+  * ''** V//rms// = V//p// **''
-For currents: \\ \\
-''**
-I//pp// = √(2) * I//rms// \\
-\\
-I//rms// = I//pp// / √(2) \\
-**''
@@ Line 45: / Line 43: @@
 After the rectifier the output voltage is a positive pulsed DC as shown in the picture below.
 {{ :other:electronics:bridge-rectifier-2.jpg?400 |}}
-=== Voltage ===
+The output voltage of the rectifier is lower +/- 1.4V lower then the input voltage. This is due to the forward-biased (conducting) voltage over two diodes. Due to voltage over the diodes the maximum peak value is:
-Due to voltage over the diodes the maximum peak value is:
-''** Vout//pp// = Vin//pp// - 2 * 0,7V **''
+  * ''** V//p//_out = V//p//_in - 2 * 0,7V **''
-The average Vdc value can be calculated with the formula below:
+The term V//in// defines the voltage coming from the secondary windings of the transformer (or input voltage). The average Vdc value can be calculated with the formula below:
+  * ''** V//dc//_out = V//avg//_out = 2 * V//p// / π **''
-''** V//dc// = 2 * V//pp// / π **''
 === Current ===
-The term V//in// defines the voltage coming from the secondary windings of the transformer (or input voltage). V//max// is the peak-to-peak value.
+Using Ohm’s law to derive the current, we should note that two types of resistance will limit the current, the load resistance (RL), and the forward resistance of the diode (Rf). Note: We can find the forward resistance using the diode’s I-V characteristic. The maximum current can be calculated with:
+  * ''** I//max// = V//max// / ( 2 * R//f// + R//l// ) **''
-''** V//in// = V//max// * sin⁡( 2π * f * T ) **''
-Using Ohm’s law to derive the current, we should note that two types of resistance will limit the current, the load resistance (RL), and the forward resistance of the diode (Rf). Note: We can find the forward resistance using the diode’s I-V characteristic.
-The maximum current can be calculated with:
-''** I//max// = V//max// / ( 2 * R//f// + R//l// ) **''
 Where R//l// is the load resistance, R//f// is the forward resistance of the diodes. V//max// is the maximum AC voltage.
@@ Line 75: / Line 63: @@
 We can improve the average DC output of the rectifier while at the same time reducing the AC variation of the rectified output by using smoothing capacitors to filter the output waveform. Smoothing or reservoir capacitors connected in parallel with the load across the output of the full wave bridge rectifier circuit increases the average DC output level even higher as the capacitor acts like a storage device.
-The formula for calculating ripple voltage is:
+For a full wave rectifier the ripple voltage can be calculated with the following formulas:
-''** V//r// = V//peak// / ( f//r// * R//load// * C ) **''
+  * ''** V//r// = V//p// / ( f//r// * R//load// * C ) **''
+  * ''** V//r// = I//load// / ( f//r// * C ) **''
-or
-''** V//r// = I//L// / ( f//r// * C ) **''
 Where:
   * V//r// is the peak-to-peak ripple voltage
-  * I//L// is the load current
+  * I//load// is the load current
-  * f//r// is the frequency of the ripple
+  * f//r// is the frequency of the ripple. Due to the rectifier this value is twice the frequency of the transformer. 50 Hz for half-wave rectification and 100 Hz for full-wave rectification.
   * C is the capacitance of the smoothing capacitor
-  * The ripple frequency, f//r//, is 50 Hz for half-wave rectification and 100 Hz for full-wave rectification
-calculate the ripple factor of the output waveform as the ratio of the ripple current (also known as the RMS current) to the DC current.
+==== Calculation of ripple Factor ====
+For a full wave rectifier with filter the ripple factor can be calculated with the following formula:
+  * ''** Ripple factor =  1 / ( 4√3fCR ) **''
-''** Ripple factor =  √ ( ( I//rms// / I//dc// )² - 1 ) **''
+Calculate the ripple factor of the output waveform as the ratio of the ripple voltage or current (also known as the RMS voltage) to the DC voltage.
+  * ''** Ripple factor =  √ ( ( V//rms// / V//dc// )² - 1 ) **''
+  * ''** Ripple factor =  √ ( ( I//rms// / I//dc// )² - 1 ) **''
+==== DC output Voltage ====
+**Please note:** the calculations below only work if the RC time is >> (x10) then the period T.
+E.g. in case of 100 hz (T=10ms) the RC should be in the range of 0,1 (100 ms) = 100 Ohm * 1000uF.
+{{ :other:electronics:rectifier-ripple.jpg?600 |}}
+For a full wave rectifier with filter the output voltage can be calculated with the following formula:
+  * ''** V//dc// =  V//p// - ( I//dc// / 4fC ) **''
+Substituting I//dc// with V//dc// / R this becomes:
+  * ''** V//dc// =  V//p// * 4fRC ) / ( 1 + 4fRC ) **''
-If you enter RMS current (I_RMS) and the DC current (I_DC), this calculator gives you the ripple factor.
+===== Transformer Selection =====
+Based on the above formulas, the table below calculates the required tranformer voltage to achieve a specific DC voltage.
+^Preferred Vdc^Stabilizer drop (V)^Vp^Rectifier Drop (V)^Trafo Vpp^Trafo RMS^
+| |  -3  | |  -1,4  | | |
+|  5  |  8  |  8,0  |  9,4  |  18,9  |  6,7  |
+|  9  |  12  |  12,1  |  13,5  |  26,9  |  9,5  |
+|  12  |  15  |  15,1  |  16,5  |  33,0  |  11,7  |
+|  15  |  18  |  18,1  |  19,5  |  39,0  |  13,8  |
+|  16  |  19  |  19,1  |  20,5  |  41,0  |  14,5  |
+|  18  |  21  |  21,1  |  22,5  |  45,0  |  15,9  |
+|  20  |  23  |  23,1  |  24,5  |  49,0  |  17,3  |
+|  24  |  27  |  27,1  |  28,5  |  57,1  |  20,2  |
 ===== Links =====
@@ Line 104: / Line 112: @@
   * https://www.studocu.com/en-za/document/central-university-of-technology/electronic-fundamentals-i/unit5-power-supply-design-3/14924637
   * https://gtuttle.net/circuits/topics/rectifiers.pdf
+  * https://www.physicsforums.com/threads/calculating-the-dc-value-of-the-output-voltage-for-a-full-wave-rectifier.1003323/
   * https://www.electronics-tutorials.ws/diode/diode_6.html
   * https://resource.download.wjec.co.uk/vtc/2016-17/16-17_1-9/gce-electronics-book-chapter-7.pdf