EDITS: 11/6/19 - Fixed broken links
As part of the analysis I was doing into the design and selection of parts, I ran up some calculations. I also validated the thermal characteristics of the key parts to see how likely they were to need heatsinking. I’ve captured, and attached, these in an Excel spreadsheet if you want to take a look and put it on Github. There are two attachments now: the first, original one, and the second, updated one - see the comment I've posted under this post. The calculations posting is broken into 3 parts so it isn't too long.
Some of the below is complicated (maths was never my strong point!) but was worth doing - it gives a clear indicators to what will need heat sinking and validated component selection. Some will need monitoring under test to determine actual performance.
Fuse Calculations
I've included a line-side fuse (before the primary transformer windings). I was initially confused at this because there seemed to be differing views on sizing it for either the output current or the input (to transformer) current. I took the view that line side was based on VA rating and load side on maximum current output.
Inputs
| Parameter | Value | Note |
|---|---|---|
| Transformer power | 60VA | Multicomp MCTA060/09MCTA060/09 |
| Transformer DC resistance | 38Ohms | From data sheet: 2x19Ohms |
| Efficiency | 88% | From data sheet |
| Vac | 240V | UK supply |
| Max Current | 3A | |
| Ambient Temperature | 25C | |
| In-rush Current | 74A | Measured in LTSpice (seems high!) |
| Duration | 4.4ms | Duration of fall from peak |
| Duration | 5.4ms | Duration of rise and fall |
| I^2t @ 4.4ms | 12.047A^2s | Common curve calculation: 0.5 * I * I * duration of fall from peak. I is the inrush current value |
| I^2t @ 5.4ms | 14.785A^2s | Curve calculation: 0.5 * I * I * duration of rise and fall. I is the inrush current value |
In determining the fuse I^2t value, the calculation depends on how duration of inrush is measured. in the inputs, I’ve measured this as a duration from peak (4.4.ms) and a duration from initial rise to the fall point (5.4ms) ostensibly to see if it made any difference in selection.
This gave me the follow values, calculated for line side and load side.
| Line Side | ||
|---|---|---|
| Fuse rating | 0.329A | VA / Vac * (1 / (1 - 2 * (efficiency / 100 ))) |
| Re-rating | 0.395A | Rerated for ambient 65C at 10% per 20C rise |
| Nearest value | 0.4A | |
| Re-rated for melting integral | 2.5A | Nearest value from data sheet that accounted for I^2t value |
| Type | Slow Blow | For in-rush current |
| Interrupt raiting | High kA | Fuse is mains side |
Load Side | ||
| Fuse required | 4.05A | Max current * 135% |
| Re-rating | 4.86A | Rerated for ambient 65C at 10% per 20C rise |
| Type | Slow Blow | For dealing with inrush current to bridge rectifier |
| Interrupt rating | High kA | Not as necessary as for line side but it would seem that fuses come with either a too low value of kA values |
I'm not intending on using a load side fuse so this calculation is really for interest.
Smoothing Capacitor Calculations
To remove/reduce ripple from rectified input.
| Parameter | Value | Note |
|---|---|---|
| Max Current | 3A | |
| Acceptable ripple | 1V | Peak-to-peak |
| Time, 50Hz | 10ms | Full wave rectifier, UK supply |
| Capacitance | 0.03F | C=IT/V |
| 30,000uF |
30,000uF seems high for 60VA although with 2x4700uF (9,400uF) LTSpice is simulating a ripple of 2V so its probably right. The choice of peak-to-peak voltage is arbitrary on my part in the sense I don't know what an acceptable value is - there are no specs on the LTC1624 to state what an acceptable range on its input is. The simulation works at 2x4700uF so I will start with that and if it causes an issue in the build then I can change it.
Thermistor Calculations
A voltage divider is used to measure resistance changes in the the thermistors which obviously causes a voltage drop. I want to make sure that this wasn't going to cause a power dissipation issue for the selected parts, exacerbated by higher temperatures.
| Parameter | Value | Note |
|---|---|---|
| Vin | 5V | |
| R2 | 10000Ohms | |
| at 25C | ||
| Thermistor Resistance | 10000Ohms | From data sheet (of candidate thermistor) |
| Vout | 2.5V | at voltage divider (Vin * R2) / (therm resistance + R2) |
| I | 0.00025A | Vin / (R2 + therm resistance) |
| Power dissipation | 0.000625W | Vout * I |
| at 100C | ||
| Thermistor Resistance | 688Ohms | From data sheet |
| Vout | 4.678V | at voltage divider |
| I | 0.000467A | |
| Power dissipation | 0.002W | |
| at 150C | ||
| Thermistor Resistance | 196Ohms | From data sheet |
| Vout | 4.903V | at voltage divider |
| I | 0.0004A | |
| Power dissipation | 0.002W |
Given the power dissipation values, the choice of thermistor is unlikely to be impacted by its dissipation constant affecting accuracy.
Next: Part Five - Design - PCBYAPS Part Three - Design - LTSpice
