Calculate Battery, Transformer, MOSFET in Inverter

In this post I have explained how to correctly calculate inverter parameters with associated stages such as battery and transformer, by calculating the matching the parameters correctly.

Introduction

Making an inverter all by yourself can be definitely lot of fun. However if the results are not satisfactory can completely spoil the whole purpose of the project.

Installing and configuring the various inverter parameter like the battery and the transformer to with the actual assembled circuit needs special care and attention for deriving optimal results from the assembly.

In this article I have explained how to calculate and match a battery and transformer wit the relevant circuit and also enlightens regarding the possible faults that might be encountered and the respective troubleshooting procedures.

The article enlightens the many newcomers with some of the important clues, which might be helpful while configuring an inverter circuit with the battery and the transformer, so that efficient and optimal results can be achieved.

Calculating Transformer and Battery Specs

While making an inverter, two calculations must be broadly taken into account, viz. the transformer and the battery ratings.

1) The transformer must be rated higher than the maximum load that is expected to be used with the inverter. For example if the intended load is 200 watts, then the transformer must be rated at minimum 300 watts. This will ensure a smooth running of the inverter and less heat generating from the transformer.

The voltage rating of the transformer must be slightly lower than the battery voltage for square wave inverters.

However, for concepts involving PWM or SPWM, it should be equal to the average voltage (x 2) applied at the gates of the MOSFETs.

This can be measured by measuring the average DC voltage applied at the gate of the MOSFETs from the oscillator stage and then multiplying it by 2. So, suppose your battery voltage is 12 V, but because of PWM your average switching voltage from the oscillator shows 3.5 V DC, that implies your transformer must be rated at 3.5 x 2 = 7V. Meaning its primary should be rated at 7-0-7 V and not 12-0-12 V.

2) And the battery Ah must be rated 10 times more than the maximum current rating of the load. For example if the battery is 12V rated and the load 200 watts, then dividing 200 with 12 gives us 16 amps. Therefore the battery Ah must be 10 times of this amp rating, that is 160 Ah. This will ensure your battery runs with a healthy 0.1C discharge rate and provides a back up of around 8 hours.

Calculating MOSFET Rating

Calculating MOSFET for an inverter is actually quite simple. One has to take into account the fact that MOSFETs are nothing but electronic switches, and must be rated just like we rate our mechanical switches. Meaning the MOSFET's voltage and current ratings must be adequately selected so that even at the maximum specified load, the MOSFET working is well within its breakdown level.

To ensure the above condition, you can refer to the datasheet of the mosfet and check the Drain-Source Voltage and the Continuous Drain Current parameters of the device, such that both these values are well above the load's maximum consumption values, or are selected with appreciable margins.

Suppose if the load is rated at 200 watts, then dividing this with the battery voltage 12V we get 16 amps. Therefore the MOSFET could be selected with voltage ratings anywhere between 24V to 36V as its Drain-Source Voltage (Vdss),  and 24 amp to 30 amp as its Continuous Drain Current (Id).

Take the example of the MOSFET in the image above, here the maximum tolerable voltage Vdss of the specified MOSFET is 75V, and maximum tolerable current Id is 209 amps, when operated with proper heatsink. It means this MOSFET can be safely used for all applications where the load wattage is not more than 14000 watts.

Although in real life the load handling capacity may be even lower than this.

As a rule of thumb, make sure the Vdds x Id value is at least 30% higher than the max load wattage, and the MOSFETs are adequately heatsinked.

This takes care of the MOSFETs, and ensures a perfect working of the devices even at full load conditions, but do not forget to mount them on appropriately dimensioned heatsinks.

After procuring all the necessary components as explained above, it would be important to get them checked for compatibility with one another.

Only the battery, which is one the most crucial member, hopefully will not require any prior checking, because the printed rating and the charged voltage conditions should be sufficient to prove its reliability. It is assumed here that the condition of the battery is good and it’s relatively new and “healthy.”

Calculating MOSFET Switching Parameters

The gate resistor affects the charging and discharging of the MOSFET's gate capacitance which determines the switching speed.

Turn-on/Turn-off Time:

t_on/off = R_g * C_g

Where:

R_g = R_g(ext) + R_g(int), the total gate resistance (external + internal).

Cg = Qg / Vgs, the equivalent gate capacitance.

V_gs is the gate drive voltage.

The peak current required to charge/discharge the gate can be calculated using the formula:

I_g = V_gs / R_g

The power dissipated in the gate resistor during switching can be calculated using the formula:

P_Rg = f_s * Q_g * V_gs

Where:

f_s is the switching frequency.

Q_g is the total gate charge.

The rate of voltage change during the switching period is:

dv/dt = I_g / C_oss

Where C_oss is the MOSFET's output capacitance.

Power losses is simply equal to the sum of conduction and switching losses.

Formula for Calculating the Conduction Losses:

P_cond = I_D² * R_DS(on) * D

Where:

I_D is the drain current.

R_DS(on) is the on-resistance.

D is the duty cycle.

Formula for Calculating the Switching Losses:

P_sw = 0.5 * V_DS * I_D * (t_on + t_off) * f_s

Where t_on and t_off are determined by R_g.

To select R_g:

Use the switching time formula:

t_on/off = R_g * Q_g / V_gs

Solving for the R_g to achieve the desired switching time.

Ensuring the gate drive current:

R_g <= V_gs / I_g(max)

Check that I_g(max) is within the capability of the driver.

Adjust for dv/dt and EMI:

Increase R_g to reduce EMI and ringing but avoid overly slow switching.

Use a fast recovery or Schottky diode with a reverse voltage rating at least equal to V_gs.

The diode allows faster turn-off while controlling the turn-on speed with R_g.

Example Calculation:

MOSFET Parameters:

Q_g = 50 nC

V_gs = 10 V

Gate driver current capability = 2 A

Calculations:

Selecting the t_on/off:

The Desired t_on/off = 100 ns

R_g = t_on / C_g = 100 ns / (50 nC / 10 V) = 20 ohms

Check I_g:

I_g = V_gs / R_g = 10 / 20 = 0.5 A (looks well within driver capacity).

Confirming the switching losses:

For f_s = 100 kHz, V_DS = 50 V, I_D = 10 A:

P_sw = 0.5 * 50 * 10 * 200 ns * 100 kHz = 0.5 W

Checking the transformer

The transformer, which is the most important component of the inverter, surely needs a thorough technical assessment. It may be done as follows:

The rating of the transformer can be best checked in the reverse order, i.e. by connecting its higher voltage winding to the AC mains input and checking the opposite winding for the specified outputs. If the current ratings of the lower voltage section are within the maximum limits of a regular multi-tester (DMM), then it may be checked by switching ON the above AC and connecting the meter (set at, say AC 20 Amp) across the relevant winding.

Hold the meter prods connected across the winding terminals for a couple of seconds to get the readings directly on the meter. If the reading matches with the specified transformer current, or at least is close to it, means your transformer is OK.

Lower readings would mean a bad or a wrongly rated transformer winding. The assembled circuit broadly needs to be checked for proper oscillation outputs across the bases of the power transistors or the MOSFETs.

This may be done by connecting the circuit to the battery, but without including the transformer initially. The checking should be done using some good frequency meter or if possible using an oscilloscope. If the above gadgets are not there with you, a crude testing can be performed using a pair of ordinary headphones.

Connect the headphone jack to the bases of the relevant power transistors; you should get a strong humming sound in the headphones, confirming a sound functioning of the oscillator stages.

The above confirmations should be enough to prompt you to configure all the sections together. Connect the transformer to the relevant transistor or the power devices terminals; make sure the power devices are correctly integrated with the oscillator stage.

Installing the Final Inverter Set up

Finally the battery may be connected to the power inputs of the above configuration, again do not forget to include an appropriately rated FUSE in series with the battery positive. The output of the transformer now may be attached with the specified maximum load and the power may be switched ON.

If everything’s is wired up correctly, the load should start operating at its full fledged power, if not, then something’s wrong with the circuit stage. Since the oscillator section was appropriately checked before the final installations, surely the fault may lie with the power device stage.

If the fault is associated with low power outputs, the base resistors may be tweaked for possible faults, or may be reduced by adding parallel resistors to their existing base resistors.

The results may be checked as discussed above, if the results are positive and if you find improvements in the power outputs, the resistors may be further modified as desired, until the expected power output is delivered.

However, this may lead to further heating of the devices and due care must be observed to keep them under check by either including cooling fans or increasing the heatsink dimensions.

However if the fault is accompanied with blowing of the fuse would mean a definite short circuit somewhere in the power stage.

Troubleshooting the Inverter Connections

The problem may also indicate a wrongly connected power device, a blown-of power device due to a possible shorting between the power device’s output terminals or the any of the terminals that needs to be perfectly kept aloof of each other.

Having explained a few of the above possibilities while configuring an inverter optimally, a thorough knowledge regarding electronic becomes an absolute necessity from the part of the individual who may be involved with the construction, without which the proceeding with the project may somehow get jeopardized.