## Mains Rectifier Calculations.

### Introduction.

Transformer and rectifier calculation is a very complex subject and is covered in ( many ) books and articles on the net.
This is a collection of LTspice files to aid in the calculation of rectifiers.
All the circuits use a transformer with 2 identical primaries and 2 identical secondaries.
Transformer losses are simulated as pure resistive losses.
The accuracy for transformers with low core losses is reasonable good ( within 5% for a 50 VA toroid I simulated and measured using data-sheet values ).
For transformers with high core losses ( like small short-circuit proof transformers ) accuracy is somewhere between very poor and not existing.
The simulations covers only steady-state conditions, so inrush current due to core-saturation is not simulated.
There are 3 circuits in each simulation file: one for nominal mains voltage, one for low mains voltage and on for high mains voltage.
The simulations can run with the transformer primaries in series, parallel or both at different mains voltages and frequencies.
All parameters for the simulations are in a standard spice .cir file that is included in the simulation as I find it easier to edit an ASCII file than a spice schematic.
The transformer parameters required for the simulation are the standard data-sheet values: nominal mains voltage, nominal loaded and unloaded secondary voltage and VA-rating.
It is possible to specify the secondary winding resistance, but if you do not, the resistive losses are split equally between the 4 windings.
Some of the outputs from the simulation are: Output voltage, Ripple voltage, Peak diode voltage, Diode current, Diode power dissipation, Capacitor peak voltage and Capacitor RMS current.

### Schematics.

Fig.1: Secondary center-tapped, bridge rectifier, dual output ( mrc_sc_br_do.asc ).

RECT? ≈ VSC * √2
Capacitor voltage rating > RECT?
Diode voltage rating > 2 * RECT?
Ripple frequency is double the mains frequency.
Risk of DC on transformer: No.

VMS is the mains voltage for series connected primaries, VMP for parallel connected primaries.
RMSER and RMPAR are the mains circuit series resistance, including the fuse.
The 3PDT switch selects between series and parallel coupling of the primaries.
RP and RS are the transformer winding resistances.
RECTP and RECTN are the rectified voltages.
FIP and FIN are the rectified, filtered voltages.
CCF?? are the rectifier capacitors.
RCF?? are the capacitor ESR. You will normally have to estimate this from the capacitor dissipation factor.
For large capacitors designed for high currents, this value is normally stated in the data-sheet.
RFP and RFN are the filter resistors. If you do not use these, set them to a low value like 1 µΩ.
ILDPG and ILDNG are constant current loads from each supply to GND.
RLDPG and RLDNG are resistive loads from each supply to GND.
ILDPN and RLDPN are constant current and resistive loads between the 2 supplies.

The only values that are easy to calculate for this circuit is the minimum required voltage rating for the capacitors and diodes.
These values are shown below each schematic.
VSC is the transformer secondary voltage at no load and at maximum mains voltage.
The "Risk of DC on transformer" tells if the rectifier and load may cause a DC current in the transformer ( not if you have DC from the mains circuit ).

Fig.2: Secondary center-tapped, half-bridge rectifier, single output ( mrc_sc_hb_so.asc ).

RECTP ≈ VSC * √2
Capacitor voltage rating > RECTP
Diode voltage rating > 2 * RECTP
Ripple frequency is double the mains frequency.
Risk of DC on transformer: No.

Fig.3: Secondaries in parallel, half-bridge rectifier, single output ( mrc_sp_br_so.asc ).

RECTP ≈ VSC * √2
Capacitor voltage rating > RECTP
Diode voltage rating > RECTP
Ripple frequency is double the mains frequency.
Risk of DC on transformer: No.

Fig.4: Secondaries in parallel, voltage doubler, dual output ( mrc_sp_vd_do.asc ).

RECTP ≈ VSC * √2
Capacitor voltage rating > RECTP
Diode voltage rating > 2 * RECTP
Ripple frequency from FIP or FIN to GND is the mains frequency.
Ripple frequency between FIP and FIN is double the mains frequency.
Risk of DC on transformer: Yes. If ILDPG and ILDNG are different.

Fig.5: Secondaries in parallel, voltage doubler, single output ( mrc_sp_vd_so.asc ).

RECTP ≈ 2 * VSC * √2
Capacitor CCF1? voltage rating > RECTP / 2
Capacitor CCF2P voltage rating > RECTP
Diode voltage rating > RECTP
Ripple frequency is double the mains frequency.
Risk of DC on transformer: No.

Fig.6: Secondaries in series, bridge rectifier, single output ( mrc_ss_br_so.asc ).

RECTP ≈ 2 * VSC * √2
Capacitor voltage rating > RECTP
Diode voltage rating > RECTP
Ripple frequency is double the mains frequency.
Risk of DC on transformer: No.

Fig.7: Secondaries in series, voltage doubler, dual output ( mrc_ss_vd_do.asc ).

RECT? ≈ 2 * VSC * √2
Capacitor voltage rating > RECTP
Diode voltage rating > 2 * RECTP
Ripple frequency from FIP or FIN to GND is the mains frequency.
Ripple frequency between FIP and FIN is double the mains frequency.
Risk of DC on transformer: Yes. If ILDPG and ILDNG are different.

Fig.8: Secondaries in series, voltage doubler, single output ( mrc_ss_vd_so.asc ).

RECTP ≈ 4 * VSC * √2
Capacitor CCF1? voltage rating > RECTP / 2
Capacitor CCF2P voltage rating > RECTP
Diode voltage rating > RECTP
Ripple frequency is double the mains frequency.
Risk of DC on transformer: No.

### Output example.

This is an example of the output from this simulation.

Circuit: Fig.1.
Transformer: 30 VA, 2x15 VAC loaded, 2x17.4 VAC unloaded, 1.4 Ω secondary resistance.
Diodes: 1N4007.
Capacitors: 1000 µF / 50 V.
Filter resistors: 10 Ω.
Fuse: Littelfuse 215.250HP ( 1.24 Ω cold resistance ).
Mains voltage: 230 VAC ±15% / 50 Hz.
Mains wiring resistance: 0.25 Ω.
Load current: 5 mA and 100 mA.

Fig.9: Example output from a simulation. The first 500 ms of a 1 s simulation shown.

 Lime: RECTP for 5 mA and 100 mA load current at 264.5 V mains. Blue: FIP for 5 mA and 100 mA load current at 264.5 V mains. Red: RECTP for 5 mA and 100 mA load current at 230 V mains. Green: FIP for 5 mA and 100 mA load current at 230 V mains. Purple: RECTP for 5 mA and 100 mA load current at 195.5 V mains. Grey: FIP for 5 mA and 100 mA load current at 195.5 V mains.

In addition to what you can plot, there is a lot of information in the Spice log file:

```Measurement: trans_sec_irms_max_h
1	1	0	1
2	1	0	1
```
This is the full load current for the transformer with a resistive load ( 2x15 V and 30 VA ).
The "_h" suffix means it is for high mains voltage. "_n" is for nominal mains voltage and "_l" is for low mains voltage.
The "_h" suffix is meaningless in this context as it is simply the the transformer VA rating divided by the secondary voltage.
However if one of the 2 following measurements exceeds this value for extended periods of time, you will melt the transformer.
```Measurement: trans_sec1_irms_h
step	RMS(i(rs1rser_h))	FROM	TO
1	0.0170957	0.9	0.99
2	0.21825	0.9	0.99
```
The RMS current in the transformer secondary 1 at 5 mA and 100 mA load.
```Measurement: trans_sec2_irms_h
step	RMS(i(rs2rser_h))	FROM	TO
1	0.0170957	0.9	0.99
2	0.21825	0.9	0.99
```
The RMS current in the transformer secondary 2 at 5 mA and 100 mA load.
```Measurement: d1p_vpeak_h
step	MAX(abs((v(rectp_h,rectac1_h))))	FROM	TO
1	55.4383	0	1
2	53.013	0	1
```
Peak voltage across D1P.
```Measurement: d1p_irms_h
step	RMS(i(d1p_h))	FROM	TO
1	0.0121817	0.9	0.99
2	0.160377	0.9	0.99
```
RMS current through D1P.
```Measurement: d1p_pavg_h
step	AVG(v(rectac1_h,rectp_h)*i(d1p_h))	FROM	TO
1	0.00190208	0.9	0.99
2	0.0449044	0.9	0.99
```
Average power dissipation in D1P.
```Measurement: ccf1p_vpeak_h
step	MAX(v(rectp_h))	FROM	TO
1	27.3516	0.9	0.99
2	26.1052	0.9	0.99
```
Peak voltage across CCF1P.
```Measurement: ccf1p_vvalley_h
step	MIN(v(rectp_h))	FROM	TO
1	27.3039	0.9	0.99
2	25.3424	0.9	0.99
```
Valley voltage across CCF1P.
```Measurement: ccf1p_vrms_h
step	RMS(v(rectp_h))	FROM	TO
1	27.3245	0.9	0.99
2	25.6945	0.9	0.99
```
RMS voltage across CCF1P.
```Measurement: ccf1p_vripple_h
step	abs(ccf1p_vpeak_h-ccf1p_vvalley_h)
1	0.0477352
2	0.762817
```
Ripple voltage across CCF1P.
```Measurement: ccf1p_irms_h
step	RMS(i(ccf1p_h))	FROM	TO
1	0.016258	0.9	0.99
2	0.192886	0.9	0.99
```
RMS current in CCF1P.
```Measurement: rfp_pavg_h
step	AVG(v(fip_h,rectp_h)*i(rfp_h))	FROM	TO
1	0.000275688	0.9	0.99
2	0.105356	0.9	0.99
```
Power dissipation in RFP.
```Measurement: ccf2p_vpeak_h
step	MAX(v(fip_h))	FROM	TO
1	27.2759	0.9	0.99
2	24.7326	0.9	0.99
```
Peak voltage across CCF2P.
```Measurement: ccf2p_vvalley_h
step	MIN(v(fip_h))	FROM	TO
1	27.2695	0.9	0.99
2	24.6315	0.9	0.99
```
Valley voltage across CCF2P.
```Measurement: ccf2p_vrms_h
step	RMS(v(fip_h))	FROM	TO
1	27.2736	0.9	0.99
2	24.692	0.9	0.99
```
RMS voltage across CCF2P.
```Measurement: ccf2p_vripple_h
step	abs(ccf2p_vpeak_h-ccf2p_vvalley_h)
1	0.00639153
2	0.101149
```
Ripple voltage across CCF2P.
```Measurement: ccf2p_irms_h
step	RMS(i(ccf2p_h))	FROM	TO
1	0.00130093	0.9	0.99
2	0.0224775	0.9	0.99
```
RMS current in CCF2P.
```Measurement: ccf2p_vvalley_l
step	MIN(v(fip_l))	FROM	TO
1	19.9166	0.9	0.99
2	17.4287	0.9	0.99
```
Valley voltage across CCF2P at low mains voltage.
```Measurement: ccf2p_vripple_l
step	abs(ccf2p_vpeak_l-ccf2p_vvalley_l)
1	0.00610924
2	0.0987072
```
Ripple voltage across CCF2P at low mains voltage.

In addition to the Spice measurements shown here, several other measurements are defined ( but commented out ) in the mrc_??_??_??_meas.cir files.

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