Digital Circuits

Input Networks and Amplifiers

The input network and amplifier perform the same functions as they do for the electronic analog meter. The input network presents a high resistance (11 megohms) to the circuit under test to keep from loading it down; it also attenuates the input voltage with the range switch setting to keep the test signal at the input of the amplifier under 1 volt. Although identical input and amplifier circuits can be used for both digital and analog meters, the example we are using demonstrates the use of an amplifier that can take up to 1 volt of input, and the ranges vary from 2 volts to 2000 volts, in multiplier ranges of 2, 20, 200, and 2000 volts. Since digital measurements use ten digits (0- 9), the counters, and especially the pulse generators deal in multiples of ten for convenience. The follower and amplifier circuits are both op-amps connected to accomplish their functions.


Op-Amps and ICs

The op-amp is a differential amplifier on an integrated circuit (IC) chip, with terminal access to all points in both stages. Connections can be made to these terminals to have the op-amp perform a wide variety of functions. It can be an ordinary amplifier with one input, in which the outputs can be inverted or noninverted or both. The two outputs can be used independently or as a differential output. The op-amp can also be used as a source follower. With some amplifiers, if the alternate input is used, the amplifier is the same, except that the inverted and noninverted outputs reverse. The two stages in the op-amp can also be used to gate an input. The input applied to the first stage will be fed internally to the second stage, which will block the signal until it receives a gate voltage.


Pulse Generators

The pulse generator circuits are the principal circuits which determine the accuracy of the digital meter. The clock is a signal generator, or stable oscillator, that creates and supplies the steady stream of pulses to the variable gate. This stable signal source is also passed through a sequence of decade dividers that each reduce the pulse frequencies to Y10 of their value.

In this example, the original clock frequency of I megahertz is subdivided three times, first to I 00 kilohertz, then to I O kilohertz, and then to I kilohertz. The subdividing can continue down to I hertz, so that a gate pulse of any width will be accessible. Also, the basic clock frequency, and all frequencies subdivided by 10, are available for use individually for selective counting in different ranges.


Oscillators and Waveshapers

The clocks and the decade dividers, as well are not usually just one stage. With the clock, for example, in addition to the oscillator, there are generally amplifiers and wave shaping circuits used to get each wave in the pulse train properly shaped. When a sine wave oscillator is used, clipper and clamper circuits, or a Schmitt trigger, are used to reshape the sine waves into square wave pulses.

There are countless varieties of oscillator circuits. The main requirement for a circuit to oscillate and produce a stream of waves is that positive feedback, also called regenerative feedback must take place. The feedback from the output must be in phase with the input for regeneration to occur. Several types of oscillators include: a two-stage oscillator, using the noninverted (in phase) output for feedback; a one-stage oscillator using RC circuits to shift the feedback phase 180 degrees to make it positive; and an LC tuned or resonant circuit to cause regenerative feedback. The tuned oscillator also has a crystal, which is not always used, but which has a natural vibrating frequency to control the oscillator.






Resistance Testing: Part 2

Circuit Tracing


As explained in the previous blog post “Resistance Testing: Part 1,” because of long lines, and because long lines can be buried or otherwise hidden from view, it is difficult to perform some tests without knowing which wires or connections are part of which circuits. A unique tracing system, which is available to quickly identify those parts on the same circuit, uses a hand-held radio transmitter and receiver to trace a circuit with radio-frequency signals. The transmitter can either be plugged into an outlet or connected anywhere in a line with alligator clips. The transmitter sends the signal along the lines to all other lines and components connected to it. The portable, hand-held receiver, which has a pickup antenna, is moved along the suspected path, whether the wires are in walls or buried, and the receiver will give an indication in the form of a light and a beeping tone when it is aimed at all the associated wires, outlets, switches, junction boxes, circuit breakers, etc.


Short Tests


When a short occurs in an electrical line, wear and abrasion of insulation on a wire generally exposes the bare conductor and allows it to contact either a grounded metal or another damaged wire. Any damage to a hot line’s insulation is likely to cause a short, since in nonmetallic sheathed cable, the grounded wire is bare, and in BX cable or conduit, the metal sheathing is grounded.

Testing for shorts is a lot like making continuity tests. If a short exists between a hot wire and ground, then an ohmmeter will show continuity along that line, through the short, and back through ground (with the power disconnected). Finding the exact location of the short is another matter. On long lines, the resistance reading of the wire and the normal ohms-per-1000 feet of the wire will be a guide to the location of the short. For relatively short lines, the signal tracer test can be used. The receiver, when moved along and near the hot line, will show signal reception before the short is reached, but the reception will fade out as the short is passed.


Open Tests


“Open” tests are continuity tests in which the user is looking for an open trouble in a circuit. Continuity, or little or no resistance, affirms a good, continuous circuit, and high or infinite resistance indicates an open circuit.

A power switch being tested with a voltmeter can be tested for continuity (with the power disconnected) with an ohmmeter in a similar way. With the ohmmeter connected across the switch terminals, the ohmmeter should read zero ohms, or continuity with the switch turned on. It will read infinite or very high resistance if the switch is bad, indicating an open circuit in the switch.




Electromagnetic Meter Construction

Permanent Magnets

The moving-coil meter movement uses a horseshoe shaped permanent magnet. The moving coil is placed within the magnetic field between the magnet’s two poles. However, if a simple horseshoe magnet were used, many of the magnetic lines of force would not cut through the moving coil. Magnetic lines of force travel the path of least resistance. Soft iron offers less resistance to lines of force than air. Therefore, soft iron pole pieces are attached to the poles of the magnet to concentrate the lines of force between the magnetic poles.

To further concentrate the lines of force between the magnet poles, a circular, soft-iron core is placed between the pole pieces. The core not only causes a very strong, uniform magnetic field between the poles, but it also acts as a keeper to help the permanent magnet retain its magnetism. The moving coil rotates around the soft iron core, which is fixed in place.


Moving-Iron Meters

The moving-coil and the moving-iron meter movements contain essentially the same parts except for the permanent magnet of the moving-coil movement and the iron bars of the moving-iron movement. A moving-iron meter contains two vanes mounted within a coil. One vane is fixed and the other, with a pointer attached, is free to rotate. Current through the coil induces a magnetic field of the same polarity in both vanes. The free vane, therefore, is repelled by the fixed vane. It rotates a distance that depends on the strength of the magnetic field, and, therefore, on the strength of the current. The pointer, which is attached to the free vane, also rotates and swings across a calibrated scale to indicate the amount of current flowing.


Iron Vanes

The differences between the concentric-vane and radial-vane iron meters are the shape of the vanes and the physical placement of the vanes with respect to each other. The concentric-vane meter contains two semicircular soft iron vanes. One vane is essentially inside the other, which is why the meter is called a concentric-vane meter. The outside vane, which is tapered at one edge, is fixed; the inner vane, which has square edges, is pivoted. When current flows through the coil, the lines of force cut through both vanes, but the distribution of the lines of force is not the same in one vane as in the other. The lines of force are distributed uniformly through the movable (inner) vane because its dimensions are uniform, but they are not distributed evenly in the stationary (outer) vane because of its tapered edge. Less lines of force pass through the tapered end than through the rest of the vane because the tapered end is smaller than the rest of the vane, and, therefore, has a higher magnetic reluctance.

When both vanes become magnetized in the same polarity, they will repel each other, causing the movable vane to rotate on its pivot. The strongest repulsion will occur in the area where the stationary vane is not tapered since there will be more magnetic lines than in the tapered area. This means that the movable vane will swing toward the tapered end of the stationary vane since there are fewer lines of force there.




Voltage Tests

Where there is an option for the types of tests or measurements that can be done, opt for the resistance check, which allows for all power to be “off. ” To play it safe in these instances, wherever possible, throw the mainline switch or associated circuit breaker off. Lock the switch off if possible or tag it. Wear clothing that covers as much of your body as possible to reduce the chances of inadvertent contact with “hot” points. Try to use one hand at a time to make connections. Wear rubber or plastic soled shoes that do not use nails and are not worn or frayed. Wear gloves for as many tests as possible and use tools that have insulated handles and test leads that are not frayed. When wiring must be disconnected for a voltage or current test, always disconnect the power before the wiring is disconnected or reconnected and discharge all   capacitors.

Be especially cautious in hazardous environments- wet locations of all kinds are dangerous: atmospheres with metal, fibers, carbon, and grain dust are explosive, and can be set off with an electrical spark or hot equipment. Be careful around dangerous fluids and fuels, and gaseous vapors.


Neon Bulb Outlet Test

Meters are usually used to make tests where rather specific, or sometimes, approximate readings are required. There are many tests that only have to indicate whether a line is “hot” or not. Low-cost devices which are easy to use are available for making quick checks like these. The neon bulb tester is one example.

The neon lamps used in line voltage testers typically will not glow if the voltage is under 80 volts and can usually be used safely with voltages up to 250 volts, and sometimes to about 500 volts. Be aware of the rating of the tester you buy. Voltages above the lamp’s upper limit will damage the tester.

The neon tester will glow when it is connected between the hot line and the ground terminals and will not glow between the grounded terminals. This is a good test to determine “hot” and grounded lines. The neon lamp has two elements in it. Only one element glows with a dc voltage, and both glow with an ac voltage.

A similar plug-in tester uses three glow lamps, which with six combinations of glow/no glow lights, can indicate whether the outlet voltage is correct, or whether there is an open ground, open neutral, open hot line, reversed hot and ground lines, or reversed hot and neutral lines.


Thermostat Voltage Test


The heating and/ or cooling system thermostats can be either a high- or low-voltage type. The high-voltage type uses the power line voltage to directly activate the equipment being controlled. This hot line test must be handled as carefully as any power line. The low-voltage variety, used in residential and small commercial applications, is like the low-voltage bell circuits. A transformer in the power line reduces the power line voltage to 24-volts dc, which requires inexpensive, safe, low-voltage wiring. The 24 volts at the thermostat is also safe to the user in the event of a short circuit with a metal thermostat case.

While high-voltage power line thermostats can control equipment directly, the 24-volt thermostat usually operates a 24-volt relay, which closes its contacts to energize a high voltage power line circuit. A meter should be used at the thermostat wire to determine the precise reading.






Electromagnetic Current Meters

How Current Affects a Magnetic Field

Current flowing through a coil produces the magnetic field that surrounds the coil. The strength of the magnetic field is proportional to the amount of current flowing through the coil. As the current increases, the strength of the magnetic field increases, and as the current decreases, the strength of the magnetic field decreases. For example, if a current through a certain coil is increased from 1 to 1.6 amperes, the magnetic field around the coil will be stronger for 1.6 amperes than it was for 1 ampere.

Now suppose a spring is attached to the iron bar so that it holds back the bar. The magnetic field, therefore, will have to overcome the spring tension. The stronger the field, the more the spring tension will be overcome. Therefore, the greater the current flowing through the coil, the greater will be the magnetic field and the further the iron bar will be drawn into the coil. The greater the current flowing through a coil enclosing two iron bars, the further each iron bar will be repelled from the other. Similarly, the moving coil will rotate further as the current through the coil increases. All electromagnetic current meters operate on the principle that the strength of the magnetic field about a coil is proportional to the amount of current flowing through it.


Types of Electromagnetic Current Meters

Magnetic fields can be used to cause motion between magnetized objects and the amount of motion is proportional to the strength of the magnetic field, which, in turn, is proportional to the current that produces the field.

There are two basic types of electromagnetic current meter movements in use today: the moving-coil type and the moving-iron type. Both types operate on electromagnetism, but each type uses magnetic fields in a slightly different way to indicate the amount of current flowing in a circuit. Also, each type has certain advantages and disadvantages.

It is not easy to tell the difference between the different types of meters just by looking at them or by using them. From the outside, they appear the same, and they are generally used in the same manner to take current measurements. But, when you know how each type works, you can easily identify them when you examine their movements.


The Moving-Coil Meter Movement

In 1882, Arsene d’Arson val, a Frenchman, invented the galvanometer, named in honor of Italian scientist Galvani. The meter was basically a device that used a stationary permanent magnet and a moving coil. Although the early galvanom­eter was very accurate, it could only measure very small currents and was very delicate. Over the years, many improvements were made that extended the range of the meter and made it very rugged.

Because it is extremely accurate and rugged, the moving-coil movement is by far the most common meter movement used today. It is the basic meter movement used to measure current, voltage, resistance, and a wide variety of other electrical quantities. Therefore, a thorough understanding of the moving­ coil meter is a “must” for anyone studying electricity.

In its simplest form, the moving-coil meter uses a coil of fine wire wound on a light aluminum frame. A permanent magnet surrounds the coil. The aluminum frame is mounted on pivots to allow it and the coil to rotate freely between the poles of the permanent magnet. When current flows through the coil, it becomes magnetized, and the polarity of the coil is repelled by the field of the permanent magnet. This causes the coil frame to rotate on its pivots, and the distance it rotates depends on how much current flows through the coil. Therefore, by attaching a pointer to the coil frame and adding a scale calibrated in units of current, the amount of current flowing through the meter can be measured.




Damping a Moving-Coil Meter


Keeping friction to a minimum permits measuring small currents, but creates a major problem when reading the meter.

When a meter measures current, the pointer should move across the scale and stop immediately at the correct reading. However, because of the very little friction of the rotating parts, the pointer does not come to rest immediately at the correct reading; it overshoots because of inertia, and then the spring pulls it back; it overshoots slightly again, and so on. As a result, the pointer tends to swing back and forth, or vibrate, about the correct reading point many times before coming to rest.

To overcome this problem, the meter movement must be damped. Damping can be thought of as a braking action on the rotating parts. It almost completely eliminates the vibrating action of the pointer, resulting in quick, correct pointer indication.

Damping also eliminates another problem. When a meter is removed from an external circuit or when the circuit is deenergized, the pointer returns to zero. Because of the very low friction of the rotating parts, the springs tend to pull the parts back to zero very quickly; so quickly in fact, that the pointer could bend as it overshoots and strikes the left retaining pin. This is particularly true when the meter returns to zero from near full -scale deflection.


Damping a Moving-Coil Meter

Moving-coil meter movements make use of the aluminum frame on which the coil is wound to provide a damping. Since aluminum is a conductor, the frame acts as a one-turn coil. When the coil assembly and pointer rotate to register current, the aluminum frame cuts through the field flux lines of the permanent magnet. Small currents, called eddy currents, are induced in the frame, which set up a magnetic field about the frame.

The polarity of this magnetic field is opposite to that of the magnetic field about the coil. Therefore, the magnetic field about the frame opposes the magnetic field about the coil. This action reduces the overall field of the moving coil so that it swings more slowly. In effect, the faster the coil swings, the more the aluminum frame’s field slows it down. This causes the coil and pointer to rotate relatively slowly and smoothly to the correct reading without vibrating. As soon as the coil assembly and pointer come to rest, no further eddy currents are induced in the frame and its magnetic field disappears.

When the meter is disconnected from the circuit, or when the circuit is deenergized, essentially the same action occurs. The coil assembly and pointer start to rotate very rapidly toward zero, but now, since it is rotating in the opposite direction, the eddy currents produced in the frame flow in the opposite direction. This results in a magnetic field with a polarity opposite to the one previously. As the springs pull the coil assembly and pointer closer and closer to zero, the like poles of the permanent magnet and the frame repel each other more and more so that the coil assembly is again braked or slowed down, and slowly comes to rest at zero. Thus, the pointer is prevented from striking the left retaining pin and, perhaps, bending around it.




RMS and Average Values of a Sine Wave

Alternating current flows periodically first in one direction and then in the opposite direction. One direction is called a positive alternation and the other direction is called a negative alternation. A complete positive and negative alternation is called one cycle. The number of complete cycles that occur each second is the frequency and is designated in hertz, abbreviated Hz. Therefore, if one complete cycle occurs per second, the frequency is 1 Hz; if 5 cycles are completed per second, the frequency is 5 Hz, and so on.

An ac wave can have many wave shapes; for example, it can be a sine wave, square wave, sawtooth wave, etc. AC meters are calibrated based on sine waves. When an ac meter is used to measure non-sinusoidal waveforms, only an approximate indication of values is obtained. Sometimes the indicator could be so far off that the reading is meaningless. Therefore, other measuring instruments such as oscilloscopes should be used instead of ac meters to measure non-sinusoidal waveforms.


 RMS and Average Values of a Sine Wave

The root-mean-square (rms) value of a sine wave is very important in the study of meters. The basic electrical units, that is, the ampere and the volt, are based on de. Therefore, a method had to be derived to relate ac to dc. The maximum, or peak, value of a sine wave could not be used because a sine wave remains at its peak value for only a very short time during an alternation. Thus, a sine wave with a peak current of 1 ampere is not equal to a dc current of 1 ampere from an energy standpoint since the dc current always remains at 1 ampere.

A relationship based on the heating effects of ac and dc was derived. It was found that a current equal to 0.707 of the peak ac wave produced the same heat, or lost the same power, as an equal de current for a given resistance. For example, a sine wave with a peak value of 3 amperes has a heating effect of 0.707 x 3, or 2.121 amperes of de.

The value of 0.707 can be derived in the following manner: The heating effect of current is based on the basic power formula; that is, P = 12 R, where P is the power dissipated as heat. From the formula, you can see that the heat varies as the square of the current.

When a sine wave reaches its peak value, the heat dissipated becomes maximum. Lesser heat values are dissipated for all values of current below the peak value. To find the heat dissipated during an entire sine wave cycle, each instantaneous value of current is first squared, and then added. Then the mean (or average) of this sum is found. After this, the square root of the mean is found, and the answer is called the root-mean-square (rms) value of the sine wave. Often the rms value of a sine wave is called the effective value because 0.707 of the peak value of a sine wave has the same effect as an equal amount of de.

Another sine wave characteristic that is important in the study of meters is the average value of the sine wave. The average value is obtained during one alternation and is equal to 0.637 of the peak value of the sine wave.




Rectifier Meters

The moving-coil meter movement can only be used to measure dc, however; there is no way that it can be used to measure ac directly. If ac was applied directly to the meter, one half of the cycle would try to make the meter pointer move in one direction and the other half would try to make the pointer move in the opposite direction. Even at very low frequencies, the pointer would not be able to move fast enough to follow the positive and negative alternations of the ac wave. Therefore, instead of moving across the scale, the pointer would simply vibrate about zero. But, if the ac is first changed to dc before applying it to the meter movement then the moving-coil meter can be used in ac applications as well as dc.

Alternating current can be converted to dc by special devices called rectifiers. These devices offer a very high opposition to current flow through them in one direction and a very low opposition to current flow in the other direction. Therefore, when a sine wave is applied to a rectifier, it will pass either the positive alternation or the negative alternation, depending upon how the rectifier is connected into the meter circuit. In no case, however, will it pass both alternations. Therefore, a rectifier changes a sine wave to a pulsating dc wave. In a rectifier symbol, the arrow points in the direction of high resistance, so current flow through it is in the opposite direction. Rectifier meters use semiconductor rectifiers.


The Half-Wave Rectifier Meter

There are two basic types of rectifier circuits: the half-wave type and the full-wave type. In the half-wave type, one alternation of current passes through the meter movement and the opposite alternation is bypassed by the rectifier. Even though current through the meter is pulsating, the meter pointer, because of its inertia, will not have sufficient time to follow these fluctuations. Therefore, the meter pointer will rest at the average value of the current flowing through it.

The average current for one alternation is 0.637 of peak value, but, for the next alternation, it is zero and that alternation is bypassed by the meter. Therefore, the average current for a complete cycle is the sum of both alternations divided by 2, or 0.637/2 = 0.313 of peak value. The meter pointer then deflects to the position on the scale that represents 0.318 of the peak value of the current flowing through the meter. But, for the reading to be meaningful the scale is usually calibrated to show the equivalent effective or rms value. Therefore, the points on the scale are calibrated at 0.707 of the equivalent peak values.




Introduction to Electromagnetism

The Basic Meter

Meters, except for the few that operate on electromagnetic principles can only measure the amount of current flowing through them. However, they can be calibrated to indicate almost any electrical quantity. For example, you know that according to Ohm’s law, the current that flows through a meter is determined by the voltage applied to the meter and the resistance of the meter: I=        V/ R

Therefore, for a given meter resistance, different values of applied voltage will cause specific values of current to flow. As a result, although a meter measures current, the meter scale can be calibrated in units of voltage.

Similarly, for a given applied voltage, different values of resistance will cause specific values of current to flow. Therefore, the meter scale can also be calibrated in units of resistance, rather than in units of current. The same holds true for power, since power is proportional to current:    P = VI or P = I 2 R


The Current Meter

When current flows through a wire, it produces three effects:

1.         It creates a magnetic field that surrounds the wire.

2.         It generates heat in the wire.

3.         It produces a voltage drop across a resistance.

The amount of current flowing through the wire determines both the strength of the magnetic field and the amount of heat produced. These effects are used in the two basic types of current meters: the electromagnetic current meter and the thermal current meter. From their names, you can see that the electromagnetic meter makes use of the magnetic field to measure the amount of current flow and the thermal meter makes use of the heat produced by the current flow to measure the amount of current flow.


Review of Electromagnetism

The electromagnetic current meter is, by far, the one used most often to measure current, voltage, resistance, and power. This type of meter is easy to understand if you know the basic magnetic principles upon which the meter operates.

Magnetic fields interact in certain ways. For example, the like poles of two iron magnets will repel each other and the unlike poles will attract each other. The same is true for the like and unlike poles of electromagnets. Furthermore, an iron magnet and an electromagnet will repel each other if they are positioned so that their like poles are facing each other, and they will attract each other if their unlike poles are facing each other.



If you place a soft iron bar close to a magnetized solenoid, the iron bar will become magnetized. The magnetic lines of force set up in the iron will line up in the same direction as those of the solenoid. As a result, the poles set up in the iron bar will also be in the same direction. Therefore, the poles of the solenoid and iron bar that face each other are opposite. Since opposite poles attract each other, the iron bar will be drawn into the coil. The plunger-type moving iron meter operates on this principle.




Calculating the Resistance of Multirange Multipliers

There are two methods of calculating the values of multiplier resistors for a multirange voltmeter. In the first method, each multiplier is calculated the same as for a single-range voltmeter. Assume that you wish to extend the range of a 1-mA movement to measure 0- 10, 0- 100, and 0- 1000 volts, and you also want a 0- 1-V range. Since full-scale deflection equals 1 Von the 0- 1-V range (V = IM RM = 0.001 A x 1000 Q = I volt), no multiplier is needed. The total resistance (RT OT) needed to limit meter current (IM) to 1 mA on the 0- 10-V range is RrnT = V w vJ IM   =   10 V/ 0.001A=    10,000 Q

Since the resistance of the meter (RM) is 1000 ohms, then the multiplier resistance RMuLT is 9000 ohms. A second method of calculating the values of voltmeter multiplier resistors is the series-multiplier arrangement in which the multiplier resistors are connected in series. R1 is the multiplier resistor for the 0-10 volt range. For the 0- 100-V range, R1 is in series with R2. Therefore, the value of the multiplier resistance for the 0- 100-V range is equal to R1 plus R2. Similarly, the multiplier resistance for the 0-1000-V range is equal to R1 plus R2 plus R3.

Now, let’s calculate the values for a series multiplier voltmeter. We will use the same 1-mA, 1000-Q meter movement that we used previously. Since this movement indicates 1 volt for a full-scale deflection, no multiplier resistor is needed for the 0- 1-V range. Therefore, your first step is to calculate the multiplier resistance needed for the 0- 10-V range. Again, using Ohm’s law, find the total resistance (RToT) needed to limit meter current (IM) to 1 mA at this range:

RrnT = V w.xl lM     = 10 V/ 0.001 A = 10,000 Q

Therefore, multiplier resistor R1 for the 0-10-V range equals 10,000n minus the 1000-Qmeter resistance, or 9000 n. Thus far, the procedure is the same as in the other method, and the value of the multiplier resistor is the same for the 0- 10-V range. Having found the series multipliers for the 0- 1- and 0- 10-V ranges, let’s calculate the total resistance needed for the 0- 100-Vrange:

RrnT = vM AXl’IM = 100 v; o.001 A = 100,000 n

Subtracting   the meter resistance from the total resistance, you find that the multiplier resistance for the 0- 100-V range is 99,000 ohms. Thus far, this method is the same as the previous, but now the multiplier resistance is made up of R I plus R2 in series. Therefore, since you need 99,000 n for the multiplier resistance and R I equal s 9000 n, R2 must equal 90,000 n.

Similarly, for the 0-1000-V range:

RT oT = VMNJ’IM = 1000 v; o.001 A = 1,000,000 n

Thus, RMuLT = RToT –   RM = 1,000,000 –   1000 = 999,000 n. But RMuLT = R1    + R2   + R3.

Thus, RMuLT =   999,000 n =   9000 + 90,000 + R3

And R3 =   999,000 –   99,000 =   900,000 n

No matter which method you use, the value of the multiplier resistance for each range remains the same. However, in the first method, the multiplier is a single resistor, while in the second method, on all but the first extended range, it is made up of resistors in series.