# Voltage Drop

Summary: Voltage Drop is the loss of voltage caused by the flow of current through a resistance. This loss, measured across the resistor, is directly proportional to the current.

 Short Definition Lower voltages at the electrical load than power source, due to resistance in the wire.

For best performance, at 5 amps a voltage drop of no more than 5% is best. The maximum acceptable voltage drop is 10% at 5A.

Most charts for bus wiring use these rules to determine the length and gauge of wire.

## Concept

Voltage Drop occurs when current flows through a conductor. It obeys Ohm's Law, where the amount of voltage is equal to the resistance multiplied by the current.

A wire has resistance, which in short runs in negligible. Over long distances it becomes an significant. Resistance is typically expressed in 'ohms per thousand feet' or another similar measure. The resistance is a function of both the diameter and length of the wire. Light gauge wires such as 22 AWG are more resistive than heavy wire such as 14 AWG typically used in house wiring.

For example, in house wiring, 14 ga is used for 15A circuits, but for 20A circuits 12 ga is specified. This is to minimize the voltage drop, and the I2R (I squared R) losses. These losses appear as heat. Too much current, too much heat, potential for a fire. (Note: these are for copper. Aluminum wire is even heavier for the same current capacity, sometimes called ampacity.)

Electrical codes specify the maximum voltage drop allowable, usually no more than 3%. If the voltage drop exceeds the specifications, changes are required. Load calculations are made prior to wiring to ensure everything meets Code. Even though the circuit is rated for 15A, codes usually only allow a maximum of 80% of the rated current, limiting the circuit to a maximum of 12A on a 15A circuit. If the load exceeds the maximum allowable current rating, an extra circuit must be installed.

For Digital Command Control this voltage drop comes into play. DCC wiring must be more robust than the older Direct Current Block wiring, as one booster may supply the entire layout. Thus, the bus wires must be heavy gauge, reducing voltage drop in the bus. Unlike old analog configurations, the booster supplies a lot more current to multiple points on the layout, instead of a small amount of current supplied to one block by a small power supply located nearby.

Voltage drop reduces the amount of voltage available to the decoder. To maintain the power output of the motor, less voltage requires more current draw to do the same work, which can result in a fried decoder. A drop of one volt between the booster and locomotive can cause problems. As stated above, a voltage drop of 5% is acceptable, and at 5A, a maximum voltage drop of 10%.

## Practice

### LEDs

An example of using Voltage Drop is LED lighting. LEDs have very strict limits on the voltage and current. The current is important, as too much will destroy the device. To limit the current, a resistor is wired in series with the LED. The resistor limits the current flow to an acceptable amount, and a voltage proportional to the current appears across the resistor.

### Bus Wiring

Since DCC uses a digital signal in the 8 to 10kHz range, wire resistance becomes more complicated. The addition of inductance and capacitance into the mix results in an Impedance, represented by Z, which is also expressed in Ohms.

DCC uses heavy gauge bus wires to distribute power to the track. At intervals, a wire is connected between the bus and the track, typically every three to six feet in HO. Since the de facto standard today is Nickel Silver rail, which has a higher DC resistance, the resulting circuit parallels the low resistance (DC) copper bus wires with the higher resistance rails. Ohm's law states that the sum of resistors in parallel is less than that of the smallest resistor. The bus wire effectively negates any resistance in the rail. Current follows the lower resistance bus wire under the track instead of relying on the track to carry all the current. Which reduces the voltage drop.

A good example of voltage drop in action is a car battery. It has a certain amount of internal resistance. Using a voltmeter it may indicate 13.2V, which is its typical no-load voltage. When a mechanic tests the battery he connects a device which has a high resistance (the voltmeter) in parallel with a low Ohm high wattage load resistor. There is a switch which must be depressed to connect the load resistor to the battery. The purpose of that load is to simulate the starter motor's current draw. By pressing the switch, a low resistance is paralleled with the voltmeter, and the voltmeter will indicate if the battery is good or not. Too much internal resistance reduces the voltage across the battery below an acceptable level, because there is not enough power available due to the internal resistance of the battery being too high, meaning the car may not start. The internal resistance of the battery not only causes a voltage drop within the battery, it also reduces the total current available. This is the typical reason why batteries or dry cells die: The internal resistance of the cell(s) increases to a point where the voltage available under load is insufficient to power the device.

In Digital Command Control, two things can happen with poor wiring or no bus wiring. The decoder overheats from excessive current draw, damaging or destroying it. Or the circuit breaker may not work as intended, failing to trip on an over current event means damaged locomotives or even wheels being welded to the track.

During the wiring phase, the track should be tested regularly. One test is the Quarter Test, named because a coin is placed across the rails. The booster should cut out immediately. If not, there is a problem with the wiring. Correct it before any damage happens.

### Voltage Drop caused by Rail Resistance

One of the reasons for using a track bus with multiple feed points is to reduce the resistance presented by the rail. Compared to an equivalent copper wire, Nickel Silver has 19 times the resistance. Nickel Silver is a copper alloy (60%), with the remainder being equal amounts of nickel and zinc. Silver, which is an excellent conductor, is not present.

Basic Rule of Electricity: Current will always seek out the path of the least resistance. Safety First: Always remember that path can be you!

By paralleling a lower resistance copper wire with a higher resistance wire (such as rail) Ohm's Law states that the resistance is
Rtotal = 1 ÷ (1/R1 + 1/R2)
Effectively making the resistance of the pair almost equal to the value of the lower resistance copper wire.

By not relying on the rail to carry all the current, voltage drop is minimized by allowing current to move to the site where it is needed using a lower resistance copper bus wire.

For more information on resistance of nickel silver rails, see the Rail Size page.

#### Example:

• 5m length of Nickel Silver C100 rail
• 5m 14AWG copper wire.
• Rail = 0.4Ω
• Copper = 0.05Ω

This may be written as 0.4Ω || 0.6Ω

This formula for calculating the equivalent resistance of two resistor in parallel can be expressed as
RTotal = (R1 –1 + R2 –1) –1

Equivalent resistances:

• Rail = 1 ÷ 0.4 = 2.5
• Copper = 1 ÷ 0.05 = 20

Sum of 20 + 2.5 equals 22.5, the result of 1/22.5 = 0.044 Ω

• X –1 is the same as 1/X. Calculators can use either symbol for this operation.

Another formula for calculating parallel resistances:
R Total = (R1 × R2) ÷ (R1 + R2)

0.4 × 0.05 ÷ (0.4 + 0.05) = 0.02 ÷ 0.45
= 0.044Ω. (Always remember the Order of Operations!)

Voltage Drop (DC Resistance)

• Rail = 0.4Ω X 2.5A = 1V
• Copper Wire 0.05Ω X 2.5A = 125mV

Rail plus Copper wire in parallel: 0.044Ω × 2.5A = 0.111V (111mV)

Exchanging the C100 rail for C70, the resistance increases to ~ 1Ω, so the voltage drop on the rail alone is 2.5V

### Effect Without a DCC Power Bus

Relying exclusively on the rails to carry the power will introduce a significant amount of voltage drop.

Using the table below, the impedance of C100 rail is 0.076Ω per metre. If the track runs 10 metres, the impedance is 0.76Ω X 2, or 1.52Ω. A one amp current will result in a 1.5V drop across the circuit. Placing a bus with an impedance of 0.55Ω in parallel with the track results in a total impedance of 0.4Ω

For easier math, without the power bus, at 1A Vdrop is 1.5V, with the power bus, VDrop is 0.4V. Without the Power Bus arrangement, the voltage drop is 3.75 times more.

Apply that to Code 80 rail: Z80 is 10 X 2 X 0.108Ω, or 20 X 0.108 = 2.16Ω. At one amp, VDrop80 = 1A X 2.16Ω = 2.16V. Multiply that by 5A and VDrop80 is now 10.8V.

## Voltage Drop - AC Measurements

Since the rail impedance is an AC measurement, it would be better to use AC equivalents for the power bus too. An Ohmmeter only measures the DC resistance, it doesn't see any inductance or capacitance present. Due to the nature of the DCC Waveform, the booster sees the track and power bus as an impedance, which is much larger than the DC resistance of the circuit. See Track Bus Impedance for more details on the power bus measurements.

The power bus is 12AWG and has an impedance of 0.55Ω/10m loop, or 20m total. (0.55-1 = 1.8.)

Rail and Bus Impedance For a 10m run (per leg), Total Z is Rail and Bus in Parallel. Both legs are the sum of the Rail A and Rail B circuit.
DCCWiki.com Voltage Drop Table
Rail Size OHMS Volts
Code Rail Impedance Bus Impedance Total Z Bus // Rail Both Legs Voltage Drop at 1 Amp
100 0.76 0.4 0.3 0.5 0.5
83 1.08 0.4 0.3 0.6 0.6
70 2.06 0.4 0.3 0.7 0.7
Calculated as follows:
• Length of power district is 10 metres
• Bus is estimated at 0.4 Ω per line
• Rail and Bus are connected in parallel, with the bus value stated above
• The result is doubled to represent the sum of both legs of the circuit
• The Voltage Drop is simply the total impedance multiplied by 1A. Multiply by 5 to see a value at 5A.
• For 1A to flow in the circuit, the sum of the loads across the booster outputs would be equal to Volts ÷ Amps
These are worst case scenarios. Most of the time your current draw will not be 5A in a given power district.
Recommended maximum VDrop for DCC Wiring should be 5%, not exceeding 10%.
Planning for the worst case is the best course of action. At some point in the future it is possible to draw enough current to create a 10% voltage drop.

Assuming HO scale with 15V on the rails, the maximum permissible voltage drop is 10%, or 1.5V. At 5% this value is 0.75V

### Code 100

Using the results found above, the C100 results at 5A exceed VDropmax of 1.5V. The same applies to C83 and C70 rail. At a lower current, such as 2A, the voltage drop is within the permissible maximum of 1.5V at V. It is also close to the value for VDrop5% at 0.8V.

### Code 83

The Vdrop for Code 83 at 5A exceeds VDropmax, but it is acceptable at 2A with a Vdrop of 1.0V.

## Notes on Voltage Drop

If you were to place a load at the end of the track (the 10m point) which causes a draw of 5A total, measuring across that load:

VLoad = Vsource − (VDropA + VDropB)

Example:

• Vsource =15V
• VDropA = 1V
• VDropB = 1V

VLoad = 15V − (1V + 1V) = 15 − 2 = 13V

Using this example, while you may measure 15V at the booster output, there will be 13V at the load. As the power (volts X amps) must stay constant, as the voltage drops the current increases.

(The total voltage must equal the sum of all the voltage drops.)

As seen through the various calculated examples, the lighter the rail, the heavier the power bus must be to counteract the increased impedance of the rail. Doing so reduces the Voltage Drop to a value within acceptable limits. This becomes more important in smaller scales with lower track voltages.

Recommended Track Voltages by Scale
DCCWiki.com
Scale Recommended Track Voltage VDrop5% VDrop10%
N 12V 0.6V 1.2V
HO 15V 0.75V 1.5V
O 20V 1.0 2.0V

## Rail Impedance

See page Rail Size for more details on the impedance of Nickel Silver Rail.

DCCWiki Rail Impedance Table
Code of Rail Impedance per metre, mΩ
100 76
83 108
70 206

Rail impedance at 1 amp, 60Hz, measurement accuracy is less than 50ppm. Different alloys and rail profiles will have different values.