\require{AMSmath} \require{eqn-number}

Avionics Power

(last update:   17 May 2012)

A problem with the Grayson Hobby GH-E200 ESC (Electronic Speed Control), is it limited "BEC" regulator.

A "BEC" is an abbreviation for Battery Eliminator Circuit. This is a misleading way of saying it has a voltage regulator output for powering avionics.

This output is quite limited. From the datasheet, and what is reported on the web site, the limitation is mostly regulator power dissipation bound. This is not uncommon with linear voltage regulators. Especially so with surface mount regulators, where the ability of the device to shed heat is more limited.

Note that, for the same current, a higher voltage drop across the regulator causes more heat to be dissipated by the regulator. This is why the number of servos the regulator can support drops as the supply voltage increases from 2S to 3S. There is more voltage at the regulator's input terminal.

The current output of the regulator is 3 amps. Is this enough?

Measurement on the bench indicate each TP SG90 servo draws the following:

At idle.

\label{eqn:TP SG90ServoIdleCurrent} I_{idle} = 98 \, mA

Stalled out (this will be the maximum).

\label{eqn:TP SG90ServoStalledCurrent} I_{stall} = 788 \, mA

From the idle and stall currents, an average current (of sorts) can be found.

\label{eqn:TP SG90ServoAvgCurrent} \begin{eqnarray} I_{avg} &=& \frac {I_{idle} + I_{stall}} {2} \\ &=& 443 \, mA \end{eqnarray}

When properly set up no servo should operate in a stalled condition. Care should be take to ensure that the throw, in each direction, never causes the servo to drive into a hard stop. If the servo is commanded to drive a hard stop, it will stall. A stalled condition is when the servo is commanded to move to a location but it physically can't get there. The motor in the servo will continue to draw as much current as it can to move the gear train but to no avail. This is said to be a stalled servo.

Most often, smaller amounts of current are drawn during movement. However, a servo moving against its maximum load will also consume high current.

The idle current isn't necessarily the holding current. Due to the gear set within the servo it requires a great deal of force to torque at the servo arm to the motor shaft. Such force, at the servo arm, can be in excess of the force required to stall the servo. Thus, once in position, the servo does not necessarily require much more than the idle current, to hold its position. This is not always the case though. Depending on servo design, vibration, and how the servo is used, some level of current, above the idle current, may be required.

An estimate of how much current will be needed for the servos can be made using $I_{avg}$ of equation \ref{eqn:TP SG90ServoAvgCurrent}.

If the number of servos is,

\label{eqn:Num of TP SG90 Servos} N_{srv} = 4

we have,

\label{eqn:TotalServoAvgCurrent} \begin{eqnarray} I_{tAvg} &=& N_{srv} * I_{avg} \\ &=& 1.772 \, A \end{eqnarray}

If the stalled current is used we have,

\label{eqn:TotalServoStalledCurrent} \begin{eqnarray} I_{tStall} &=& N_{srv} * I_{stall} \\ &=& 3.152 \, A \end{eqnarray}

Note that the current in equation \ref{eqn:TotalServoStalledCurrent} is slightly more than the rating of the BEC output of 3 amps. However, this presumes that all $N_{srv}$ servos are stalled. In practice this is not likely, given proper model setup.

Although the current in equation \ref{eqn:TotalServoStalledCurrent} is higher than the GH-E200 BEC's limit, it is consistent with the four servo limit stated in the datasheet, and on the web site. However, this is true only if a 2S battery is used. If a 3S battery is used only three servos are recommended.

Why might this be?

It helps to look at the regulator power dissipation.

Each cell in a LiPo battery is rated at,

\label{eqn:VPC_LiPoCell} VPC_{LiPo} = 3.7 \, V

The 2S battery voltage output is rated at,

\label{eqn:Vout2Sbattery} \begin{eqnarray} V_{2S} &=& 2 * VPC_{LiPo} \\ &=& 7.4 \, V \end{eqnarray}

The power dissipated in a DC electronic circuit is the product of the voltage, and the current. However, in this case, the voltage used isn't $V_{2S}$. The voltage is the output voltage of the voltage regulator in the BEC or about $5\,V$.

\label{eqn:VregOutputVoltage} V_{reg} = 5 \, V

But there is one more thing... The regulator doesn't dissipate power at its output. The load connected to it does but the regulator doesn't.

So what power does the regulator dissipate?

#### The power the voltage regulator (BEC) does dissipate

A voltage regulator converts one voltage to another. Along with the output current, it is the difference between what voltage is at its input, and its output voltage that matters. This voltage difference, along with the current drawn from its output, defines the power dissipated by the regulator. So...

#### Calculating the voltage regulator (BEC) power dissipation, 2S case:

The total maximum power dissipated in the regulator, in the 2S case is,

\label{eqn:Power2Sbattery} \begin{eqnarray} PDR_{tMax2S} &=& \left[ V_{2S} - V_{reg} \right] * I_{tStall} \\ &=& \left[ 7.4 \, V - 5 \, V \right] * 3.152 \, A \\ &=& 7.6 \, watt \end{eqnarray}

Power dissipation of equation \ref{eqn:Power2Sbattery} is reasonable for a small surface mount circuit.

#### Calculating the voltage regulator (BEC) power dissipation, 3S case:

OK, how about the 3S case.

\label{eqn:Vout3Sbattery} \begin{eqnarray} V_{3S} &=& 3 * VPC_{LiPo} \\ &=& 11.1 \, V \end{eqnarray}
\label{eqn:Power3Sbattery} \begin{eqnarray} PDR_{tMax3S} &=& \left[ V_{3S} - V_{reg} \right] * I_{tStall} \\ &=& \left[ 11.1 \, V - 5 \, V \right] * 3.152 \, A \\ &=& 19.2 \, watt \end{eqnarray}

Now the power dissipation, shown in equation \ref{eqn:Power3Sbattery}, is much higher. Given the small size of the ESC, and the materials used to construct it, this is too much power. Indeed the overall dimensions of the GH-E200 are similar in size to heat sinks used to dissipate half (about 8 watts) that amount of power.

The amount of power dissipated by the regulator in the 3S case, shown in equation \ref{eqn:Power3Sbattery} is too high. When all four servos are stalled, the voltage regulator will overheat and fail. If that happens all control over the aircraft will be lost.

## Is there really a problem here?

The questions remain...

How likely is it that all four servos will stall?

And:

If they operate at reasonable current draw, will the GH-E200's BEC be able to cope?

To answer this question further testing is needed. One test, although perhaps not the most realistic in this case, would be to find the average current a servo (TP SG90) consumes while working against its rated load (torque: 1.2 kg/cm, 1.8 kg/cm stall). However, operation near the rated load is likely to yield currents at or near the stall current. Experience suggests that the loads on the servos, of an adequately constructed design, should be well below the rated torque. Perhaps far below.

It does not take much force to move the control surfaces of a small "park flyer" class aircraft. Nor does it require much force to hold the position of such control surfaces against the force of the slipstream.

Unfortunately Grayson does not offer much more in the way of engineering data, so current figures and whatnot will have to be found by testing.

The receiver is on the left, and the green vice is clamped (gently) onto a TP SG90 servo. In the background, covered in blue shrink wrap, is a Grayson GH-E200 electronic speed control.

Above is the servo load. The load is a wrench socket of about 170 gm. The push rod is positioned about 11 mm away from the center of the servo drive shaft. The torque applied to the servo drive shaft using this weight is,

\label{eqn:ServoTestJigLoad} \begin{eqnarray} T &=& 170\,gm * 11 \, mm \\ &=& 187 \, gm \cdot cm \\ &=& 2.597 \, in \cdot oz \end{eqnarray}

Neglected is the mass of the wire, and the push rod used to hang the socket.

Note that when the servo arm moves downward the torque is helping move the servo output shaft. This is not a bad aspect of the simulation. If the servo deflects a flight control surface into the slip stream, the force against the surface, in a similar way, will aid the return of the servo to the neutral position.

Also the servo showed no sign of slipping while the power was off, and the idle current was the same as the no load idle current. This means the servo did not have to work to maintain its position, despite the 187 gm-cm of torque trying to change its position.

The test jig was powered up, using an 11.1 volt, 1600 mAh battery, and operated for about one minute. During this time the arm was asked, using a JR-378 transmitter, to move back and forth at about a 1 second interval. Recording the use of current was a Fluke 87 DMM (Digital Multi Meter).

The Fluke 87 DMM logged the following:

Roughly the same test was made without the 170 gm load, witch logged the following currents:

These are single servo numbers. To estimate the in flight current load, just multiply by the number of servos. In this case $N = 4$, and I'll use the average loaded current.

\label{eqn:ServoTestJigSweptLoad} \begin{eqnarray} I_{fe} &=& N * I_{avg}\\ &=& 4 * 280 \, mA \\ &=& 1.120 \, A \end{eqnarray}

This is a far more modest current burden for the GH-E200 electronic speed control avionics voltage regulator (BEC) output. Recall that the GH-E200's avionics regulator (BEC) is rated for 3 amps. Thus there is quite a bit of headroom (1.88 amps), despite using 4 servos.

Unfortunately current isn't the only issue. The power dissipation in the regulator is what determines its survivability.

Recall the maximum power that the GH-E200's BEC can tolerate in equation \ref{eqn:Power2Sbattery}. This was about $7.6 \,W$. Let's compare that with the power dissipated in the regulator with this more modest current ($PDR_{fe}$).

\label{eqn:ServoTestJigSweptLoadPower} \begin{eqnarray} PDR_{fe} &=& \left[ V_{3S} - V_{reg} \right] * I_{fe} \\ &=& \left[ 11.1 \, V - 5 \, V \right] * 1.120 \, A \\ &=& 6.832 \, watt \end{eqnarray}

Compare the 6.8 W result of equation\ref{eqn:ServoTestJigSweptLoadPower}, with the 19 W figure of equation\ref{eqn:Power3Sbattery}. Clearly taking the time to make a realistic test was worth the effort. The situation has gone from certain failure to likely operation.

There is now almost a full watt of headroom over the 2S battery case. This will likely be serviceable. Especially if the GH-E200 is kept cool.

Remember though, none of the servos must be allowed to stall!

The key to this analysis is recognizing the importance of establishing the results of equation\ref{eqn:Power2Sbattery}. This power level (7.6 W) is what the manufacturer believes the avionics regulator can handle reliably. As long as every effort is made to keep the power dissipation in the regulator at or below this level, it should remain equally reliable. This presumes that the manufacturer's choice of 7.6 W is appropriate.

#### Reliability.

In the final analysis, what matters most is reliability. Manufacturers are providing some level of reliability, when they specify operating conditions. Often, as is the case with the GH-E200 specs. there isn't enough detail to make a judgment as to how reliable the system will be. One is left to guess.

In the final analysis, it is almost always safer to go ahead, and use a separate avionics power source. This is especially true with electronic speed controls. If the ESC fails it may take out your avionics power. The aircraft will surely crash.

Reliability is often best attained using redundancy. In this strategy perhaps both a separate avionics battery, and regulator may be used. In this way if the ESC fails, the separate avionics regulator will be unaffected. If both the ESC, and the separate regulator fail, the battery will keep the avionics active. In this way multiple failures of "reliable" systems must happen before control is lost. If each of these systems has a low probability of failure, and the failure of one will not effect the operation of another, it is highly unlikely that catastrophic loss of control will occur.

A triple redundancy system, as just described, is not trivial to design. Some careful thought must be made, as to the interaction of the three layers. If all that is done is to wire things up in parallel, the results may well be worse than any one of the systems operating on its own.

## Alternatives to the GH-E200 on board avionics regulator (BEC).

One of easiest ways around the problem of overloaded voltage regulators (BECs) is to purchase a third party BEC. Grayson Hobby has several voltage regulators (BECs) to choose from, as do other vendors (HobbyPartz (BECs), Tower Hobbies (BECs), Horizon Hobby (BECs)).

These off the shelf devices are mostly plug and play, and offer a quick solution to designs with higher power avionics needs.

However, the question remains... How do such devices work, and is it possible to build your own?