Tag Archive | "series"

Review – Agilent Infiniivision MSO-X 3024A Mixed Signal Oscilloscope

Hello Readers

In this article we examine the Agilent Technologies Infiniivision MSO-X 3024A Mixed Signal Oscilloscope. Please note that the review unit has the latest version 2.0 firmware (existing owners can upgrade with the free download).

Initial Impressions

Unlike smaller instruments the packaging is plain and non-descript, however the MSO is protected very well for global shipping and arrived in perfect condition. Inclusions will vary depending on the particular model, however all come with a calibration certificate, user guide on CD and a power lead.

image1

Four passive 300MHz probes are included with the MSO-X3024A:

image1a

Due to the constant upgrading of the firmware the lack of a printed user manual is no surprise. You can download the manual as well as the service, programming and  educational lab guides from the documents section of the product web page – which make good reading to get a feel for the unit.

Now for a tour around the unit. Coming from a smaller DSO or an analogue model, the first thing that strikes you is the display. 8.5” diagonal with 800×480 resolution:

image2

Unlike cheaper brands the larger screen is not extrapolating data from a smaller image – each pixel is separately used. The front panel is clean and uncluttered. Each button and knob feels solid and responsive, and if pressed and held down, a small help window appears with information about the item pressed. Note that each analogue channel has independent controls for vertical position and V/div sensitivity (the minimum sensitivity is 1mV/division). This saves a lot of time and possible confusion when working on time-sensitive applications.

Around the back we find the cooling van ventilation on the left, the IEC AC power socket on the bottom-right, manufacturing data and so on. The fan is just audible, however the noise from a desktop computer drowns it out. On the far right near the top are separate USB connections for device and host mode, and the external trigger input and output sockets. Apart from the trigger out signal the socket can also be set to give a 5V pulse on a mask test failure or the optional WaveGen sync pulse.

image3

Below this is a space for a Kensington lock cable, and the optional modules – the VGA/LAN adaptor or the GPIB bus module. On the right is my old faithful GW 20 MHz analogue CRO. Finally, there is a compartment on the top of the unit that can hold two probes comfortably, and four at a pinch:

image4

As the unit is can be considered a small computer, it takes time to boot up – just over thirty seconds. (The operating system is Windows CE version 6.0). The user-interface is quite simple considering the capability of the unit. The six soft-keys below the display are used well, and also can call a separate list of options under each button.

When such a list is presented, you can also use the “Push to select” knob on the right hand side of the display to select an option and lock in by pressing the knob in. Below the soft keys from left to right are: BNC output for the optional function generator, digital inputs for logic analyser, USB socket for saving data to a USB drive, probe points for calibration and demonstration use, and four probe sockets. Connections exist that can interface with optional Agilent active probes.

Specifications

This instrument falls within the range of Agilent’s new Infiniivision 3000-series oscilloscopes. The range begins with the DSO-X3012A with 100MHz bandwidth and two channels, through to the DSO-X3054A with 500 MHz bandwidth and four channels. Furthermore the range is extended with the MSO-X models that include a sixteen channel logic analyser.

Some of you will know there is also the Infiniivision 2000-series, and wonder why one would acquire a 3000-series. There are three excellent reasons for doing so:

  1. Waveform update rate is 50000 per second on a 2000, one million per second on a 3000;
  2. Memory depth on a 2000 is 100 kilopoints; 3000s have 2Mpts standard or 4Mpts optional;
  3. Eight vs. sixteen digital channels when specified as an MSO-X model.

For a full breakdown of specifications please download the Agilent data sheet located here.

Getting Started and general use

The process from cutting open the packaging to measuring a signal is quite simple – just plug it in, connect probes and go – however some probe compensation is required, which is explained quite well in the manual. There are strong tilting bales under the front side which can be used to face the unit upwards. At this point the unit is ready to go – you can start measuring by using the Auto Scale function and let the MSO-X3024A determine the appropriate display settings.

However there is no fun in that – the vertical scale can be manually adjusted between 1 mV and 50V per division, the horizontal between 2 nanoseconds and 50 seconds per division. These values can be selected rapidly or (by pressing the knob in) in a fine method for more precise values. If working with more than one channel, each can be labelled using a pre-set description or select a label from a list. One can also alter the display between X-Y, horizontal and roll modes.

Each channel has separate controls for coupling – DC/AC but no GND, as the earth point is shown on the LCD. Impedance can be 1M or 50 ohm. One can also limit bandwidth to 20MHz to remove high-frequency interference.

Capturing data is very easy, you can save images as .png or .bmp files in grey scale or colour , data in .csv form and so on. You can also assign popular functions to a “Quick Action” button – one press and it is done. For example I use this as a “save bitmap” button to send the screen image to the USB drive. If the optional LAN/VGA module is installed screens can be captured by the host computer via the network. Finally there is a very basic file explorer available to find files on the USB drive as well.

Waveforms can also be stored and used later on as references for other measurements. When reviewed they appear as an orange trace – for example R1:

rrr

The horizontal zoom mode activated using keys to the right of the horizontal control is very useful. Agilent call this “Mega Zoom” and it certainly works. Consider the following screen shot – the 32.768kHz square-wave from a Maxim DS1307 real-time clock is being analysed:

megazoom

The time base is 10uS per division – and using the zoom we can get down to two nanoseconds per division and investigate the ringing on fall of the square-wave. This is great for investigating complex signals over short periods. Awesome.

Capturing infrequent events is made simple by the combination of the one million waveforms per second sampling rate, and the use of infinite display persistence. In the following example a clock with very infrequent glitch is being sampled. By setting persistence to infinite, as soon as the infrequent glitch occurs it can be displayed and held on the screen. For example:

infreq

Triggering

There is a plethora of triggering options available. Standard modes include: edge, edge then edge, pulse-width (customisable), pattern trigger (for logic analyser – you can create your own patter of high, low, or doesn’t matter with comparison operators for duration), hex bus trigger, OR trigger, customisable rise/fall time trigger, nth edge burst trigger which allows  you to nth edge of a burst after an idle time, runt trigger on positive or negative pulse, setup and hold trigger, on video signals (PAL, PAL-M, NTSC, SECAM), and USB packets. Phew. Furthermore, if you have any of the optional decoding and analysis licenses, they include triggering on the matching signal type (see later).

Math modes

Performing math waveforms on analogue channels is done via a seperate Math button, and the operations available are addition, subtraction, multiplication, differentiation, integration, square root and FFT.

Waveform statistics

When the time comes to further analyse your measurement data, there area variety of measurements that can be taken, and they can be displayed individually, such as in the following:

stats1

or all in a summary screen:

allstats

Or you can manually use the cursors to determine information about any part of a wave form, for example:

cursors

Logic Analyser

Everything required is included with the MSO-X3024A for the sixteen channel logic analyser, including a very long dual-head probe cable:

lacables

as well as sixteen grabbers and some extension runs:

lacables2

Setup and use was surprisingly simple, just connect the probe cable head to ground, insert grabbers onto the ends of each channel wire, and connect to the signal pins to analyse. You can have all sixteen channels and the four analogue channels active at once, however when doing so the screen is quite busy. You can adjust the height  for each digital channel. Here we are measuring two analogue and eight digital channels:

msoinaction

As always there are many forms of customisation. Automatic scaling is available the same as analogue measurement. You can set the threshold levels for high and low, and presets exist for TTL, CMOS, ECL and your own custom levels. The cable is very well-built (made in the USA) and the socket on the MSO is a standard, very solid IDC connector. Thanks to the use of the IDC connector you could also make your own probes or extension cable for the analyser. Digital channels can also be combined and displayed as a data bus, with the data values shown in hexadecimal or binary – for example:

hexbus

binbus

Options

Both the 2000- and 3000-series Infiniivision units have a variety of options and upgrades available either at the time of purchase or later on. Agilent have been clever and installed all the software-based options in the unit – when required they are “unlocked” by entering a licence key given after purchase. Trial 14-day licenses are generally available if you want to test an option before purchase. You can also upgrade the bandwidth after purchase – for example if you started with a 100MHz a licence key purchase will upgrade you to 200MHz , or 350 to 500MHz. However if you wish to upgrade a 200MHz to 350/500, this needs to be performed at at Agilent service facility. Surprisingly the logic analyser upgrade that converts a DSO-X to an MSO-X is user-installable. For more information on the upgrade options and procedures please visit here.

Memory Upgrade (DSOX3MEMUP)

A simple yet useful option – it doubles the total memory depth to 4 Mpts interleaved.

LAN/VGA Module (DSOXLAN)

This options really opens up the MSO to the world (and is a lot of fun..) – it is inserted into the port at the rear of the unit:

lanvga1

VGA output is very simple – no setup required. Just plug in your monitor or projector and you’re ready to go -for example, with a 22″ LCD monitor:

monitorview

The educational benefits of the LAN/VGA module are immediately apparent – instead of having twenty classmates huddle around one MSO while the instructor demonstrates the unit, the display can be show on the classroom projector or a large monitor. The MSO display is still fully active while VGA output is used.

LAN connection via Ethernet was also very simple. The MSO can automatically connect to the network if you have a router with DHCP server. Otherwise you can use the Utility>I/O>LAN Settings function to enter various TCP/IP settings and view the MSO’s MAC address.

Once connected you can have complete control of the MSO over your network. Apart from saving screen shots:

remotesaveimage

There is a “simple” remote control interface that contains all the controls in a standard menu-driven environment:

simpleremotepanel

Or you can have a realistic reproduction of the entire MSO on your screen:

fullremotepanel

The full remote panel is completely identical – it’s “just like being there”. The ability to monitor your MSO from other areas could be very useful. For example using the mask testing in a QC area and watching the results in an office; or an educator monitoring students’ use of the MSO.

Furthermore you can view various data about the MSO, such as calibration date and temperature drift since calibration, installed options, serial number, etc. remotely via the web interface.

GPIB Module (DSOXGPIB)

This allows you to connect your MSO to an IEEE-488 communications bus for connection to less contemporary equipment.

Segmented Memory Option (DSOX3SGM)

This options allows you to capture infrequent multiple events over time. For example, you want to locate some 15 mS pulses that occur a few times over the space of an hour. All you need to do is set the triggering to pulse-width, specify the minimum/maximum pulse width to trigger from, then hit Acquire>Segmented, the number of segments to use and you’re off. When the pulses have been captured, you can return and analyse each one as normal. The unit records the start time and elapsed time for each segment, and you can still use zoom, etc., to examine the pulse. For example:

segment

Embedded Serial Triggering and Analysis (DSOX3EMBD)

Debugging I2C and SPI buses are no longer a chore with this option. For example with I2C just probe you SDA and SCK lines, adjust the thresholds in the menu option and you’re set. Apart from displaying the bytes of data below the actual waveform, there is a “Lister” which allows you to scroll back and forth along the captured data along with correlating times. In the following example a Maxim DS1307 RTC IC has been polled:

i2c_lister

The Lister details all – in the example we sent a zero to address 0x68, which caused the DS1307 to return the seven bytes of time and date data. This is an extremely useful option and is very useful when working with a range of sensors and other parts that use the I2C bus. The SPI bus analysis operates in exactly the same manner. Adding this option also allows triggering on I2C data as well.

FlexRay Triggering and Analysis (DSOX3FLEX)

The optional FlexRay measurement applications offer integrated FlexRay serial bus triggering, hardware-based decoding and analysis. The FlexRay measurement tools help you more efficiently debug and characterize your FlexRay physical layer network by having the ability to trigger on and time-correlate FlexRay communication with your physical layer signals. So if you are working on the ECU of your Rolls-Royce or new BMW 7-series, you can use an MSO that matches the quality of the vehicle under examination. Here is an example of the FlexRay being monitored in the lister:

flexray

RS232/UART Serial Decode and Trigger (COMP/MSOX3000-232)

This option allows RS232, 422, 485 and UART decoding and triggering, as well as the use of the Lister to analyse the data. For example:

uartdecode

Advanced Math (DSOX3ADVMATH)

This option adds more math functions to enhance your waveform analysis, including: divide, base-10 logarithm, natural logarithm and exponential.

CAN/LIN Triggering and Serial Decode (DSOX3AUTO)

Again, allows decoding of automotive CAN and LIN bus signals, and the use of the Lister. For example:

can_decode

lin_decode

Military Standard 1553 and ARINC429 Standards Serial Triggering and Decoding (DSOX3AERO)

The option exists for decoding and triggering of the above bus types. According to Agilent the Mil-STD 1553 serial bus is primarily used to interconnect avionics equipment in military aircraft and spacecraft(!). This bus is based on tri-level signaling (high, low, & idle) and requires dual-threshold triggering, which the 3000X supports. This bus is also implemented as a redundant multi-lane bus (dual-bus analysis), which is also supported by the 3000X.

The ARINC 429 serial bus is used to interconnect avionics equipment in civilian aircraft (Boeing & Airbus). This bus is also based on tri-level signaling (high, low, & null) and requires dual-threshold triggering, which the 3000X supports. Since ARINC 429 is a point-to-point bus, multi-lane analysis is also required to capture both send and receive data. So if you need this capability – Agilent has you covered.

milbus

Video Triggering and Analysis Application (DSOX3VID)

The DSOX3VIDEO option provides triggering on an array of HDTV standards, including:

  • 480p/60, 567p/50, 720p/50, 720p/60
  • 1080i/50, 1080i/60
  • 1080p/24, 1080p/25, 1080p/30, 1080p/50, 1080p/60
  • Generic (custom bi-level and tri-level sync video standards)

The 3000X Series oscilloscope already comes standard with NTSC, PAL, PAL-M, and SECAM support. Example of video analysis:

dsox3vid

Audio Serial Triggering and Analysis (DSOX3AUDIO)

And not surprisingly this is an option to allow decoding of and triggering from I2S digital audio data. For example:

i2s_decode

Mask Limit Testing (DSOX3MASK)

This is another interesting and useful option, idea for quality testing, benchmarking and so on. First you create a mask by measuring the ideal waveform, and then feed in the signal to be compared with the ideal mask. Mask limit testing can operate at up to 280000 comparisons per second. You can view pass/fail statistics, minimum sigma and so on, for example – a perfect test:

mask1

… then a change of frequency for a few cycles:

mask2

Furthermore you can specify the number of tests, change source channel, specify action upon errors, etc. Finally you can create and save to USB your own mask file for use later on – which can also be modified on a PC using any text editor software. Or for other monitoring options the external trigger socket on the read of the MSO can be configured to give a 5V pulse on a mask test failure.

If you have the LAN/VGA module you could place the MSO on in a lab or factory situation and monitor the testing over the network using a PC – very handy for QC managers or those who need to move about the workplace and still monitor testing in real time.

20MHz Function Generator/Arbitrary Waveform Generator (DSOX3WAVEGEN)

The “WaveGen” function is a versatile option that offers a highly controllable 20 MHz function generator and arbitrary waveform generator. It offers eleven different types of waveform: sine, square, ramp, pulse, DC, noise, sine cardinal, exponential rise and fall, cardiac and gaussian pulse.

The frequency can be adjusted between 100mHz to 20 MHz in 100 mHz steps; period from 50ns to 10s; full offset, amplitude and symmetry control; as well as logic level preset outputs (such as TTL, CMOS 5V, 3.3V etc.) Finally the WaveGen can be operated independently to normal measurement tasks, which is useful for ideal vs. actual comparisons and so on. Output is from the BNC socket at the bottom-left of the front pane and sync is also availble from the rear BNC socket. The arbitrary waveform generator is very simple to use  – and copied waveforms can be edited or have noise added to them to replicate real-world waveforms.

Power Measurement (DSOX3PWR)

This is a power measurement and analysis option that is integrated into the unit and provides a quick and easy way of analysing the reliability and efficiency of switching power supplies. It also includes a user license for U1881A-003 PC-based power measurement and analysis software that provides even more powerful insight into power supply measurement. With this option you can:

  • Measure switching loss and conduction loss at the switching device (to help improve efficiency)
  • Analyse dI/dt and dV/dt slew rate (for reliable operation)
  • Automate oscilloscope set-up for ripple measurements (to eliminate tedious manual oscilloscope set up)
  • Perform pre- compliance testing to IEC 61000- 3- 2 standards (to reduce compliance testing time)
  • Analyse line power with total harmonic distortion, true power, apparent power, power factor, and crest factor tests (to quickly provide power quality information)
  • Measure output noise (ripple)
  • Analyse modulation using the on- time and off- time information of a Pulse Width Modulation (PWM) signal (to help characterize the active power factor)
  • Measure how well a circuit rejects ripple coming from the input power supply at various frequencies with the Power Supply Rejection Ratio (PSRR) measurement.
For more indepth explanation of this option download and read the well written manual.

Etch-a-sketch

Well not a feature as such, but it exists if you know where to find it:

msoxes

Initial Conclusions

There is no doubt that the Infiniivision 3000-series are a great line of instruments. The waveform sample rate, memory size and bandwidth options are very competitive, and the ability to add various options is convenient and also helps lower the final cost for purchasing departments. (Start with the base model then hit them up for the options over time)

However there are a few things that could use improvement. Although the display is excellent – the right-hand column with “Agilent” at the top is always displayed. This is a waste of LCD space and there should be an option to turn it off, allowing waveforms to be displayed across the entire screen. If a $400 Rigol can do this, so should a $5000+ Agilent. The build unit of the unit is good, no problems are evident however it could be a little more “solid”; and the option of a clear shield for the LCD would be a great idea to protect against forceful and dirty fingers.

Furthermore the ground demonstration terminal suffers from metal fatigue very quickly, it already is somewhat chipped and may need replacing if you used it quite often. Finally, it would have been nice to see Agilent include the a carry bag – already people have asked to borrow the unit and to wander around with it in the box is somewhat awkward.

For those who rely on their test equipment will have the peace of mind that Chinese discount suppliers cannot give you – Agilent support exists and will not ignore you once a sale has been made. It doesn’t take long to find a tale of woe on an Internet forum from someone who imported their own “high-spec” DSO via eBay or direct east-Asian sellers only to find there are no firmware updates, competent English-speaking support or warranty of any kind. Furthermore, the ability to combine many functions in the one piece of equipment saves space, time and reduces your support channel back to one supplier. There is also an iPhone “app” that may be of interest – however as an Android user I haven’t tried it.

The saying “Quality is remembered long after price is forgotten” certainly holds true – and at the end of the day combined with the mix of standard and optional features at various price points – the Agilent Infiniivision MSO-X 3024A rises to the top echelon of test equipment.

 The Agilent Technologies Infiniivision MSO-X 3024A Mixed Signal Oscilloscope used in this review is a promotional consideration received from Agilent and element-14 via their Road Test program.

Agilent Test and Measurement equipment is available from your local element-14Farnell or Newark distributor.

Australian readers please note:  Trio Smartcal are the exclusive Australian Agilent distributors for all states except WA and NT – telephone 1300 853 407.

Measurement Innovation for WA and NT – telephone 08 9437 2550

High-resolution images are available on flickr.

Once again thanks for reading, have fun and keep checking into tronixstuff.com. Why not follow things on twitterGoogle+, subscribe  for email updates or RSS using the links on the right-hand column, or join our Google Group – dedicated to the projects and related items on this website. Sign up – it’s free, helpful to each other –  and we can all learn something.

Posted in agilent, DSO, MSOX3024A, oscilloscope, review, test equipment, tutorial

Electronic components – the Resistor (Part Three)

Hello readers

Today we conclude the series of articles on the resistor. You may also enjoy part one and twoWith regards to this article, it is only concerned with direct current (DC) circuits.

Pull up and pull down resistors

When working with digital electronics circuits, you will most likely be working with CMOS integrated circuits, such as the 4541 programmable timer we reviewed in the past. These sorts of ICs may have one or more inputs, that can read a high state (like a switch being on) or a low state (or like a switch being off). In fact you would use a switch in some cases to control these inputs. Consider the following hypothetical situation with a hypothetical CMOS IC in part of a circuit from a hypothetical designer:

cir1

The IC in this example has two inputs, A and B. The IC sets D high if input A is high (5V), and low if A is low (0V). The designer has placed a button (SW1) to act as the control of input A. Also, the IC sets C high if input B is low (0V) or low if it is high (5V). So again, the designer has placed another button (SW2) to act as the control of input B, when SW2 is pressed, B will be low.

However when the designer breadboarded the circuit, the IC was behaving strangely. When they pressed a button, the correct outputs were set, but when they didn’t press the buttons, the IC didn’t behave at all. What was going on? After a cup of tea and a think, the designer realised – “Ah, for input A, high is 5V via the button, but what voltage does the IC receive when A is low? … and vice-versa for input B”. As the inputs were not connected to anything when the buttons were open, they were susceptible to all sorts of interference, with random results.

So our designer found the data sheet for the IC, and looked up the specification for low and high voltages:

lowhigh1

“Aha … with a supply voltage of 5V, a low input cannot be greater than 1.5V, and a high input must be greater than 3.5V. I can fix that easily!”. Here was the designer’s fix:

cir2

On paper, it looked good. Input A would be perfectly low (0V) when the SW1 was not being pressed, and input B would be perfectly high (connected to 5V) when SW2 was not pressed. The designer was in a hurry, so they breadboarded the circuit and tested the resulting C and D outputs when SW1 and SW2 were pressed. Luckily, only for about 30 seconds, until their supervisor walked by and pointed out something very simple, yet very critical: when either button was pressed in, there would be a direct short from supply to ground! Crikey… that could have been a bother. The supervisor held their position for a reason, and made the following changes to our designer’s circuit:

Instead of shorting the inputs straight to supply or earth, they placed the resistors R1 and R2 into the circuit, both 10k ohm value. Why? Looking at SW1 and input A, when SW1 is open, input A is connected to ground via the 10k resistor R1. This will definitely set input A to zero volts when SW1 is open – perfect. However when SW1 is closed, input A is connected directly to 5V (great!) making it high. Some current will also flow through the resistor, which dissipates it as heat, and therefore not shorting out the circuit (even better). You can use Ohm’s law to calculate the current through the resistor:

cir3

I (current) = 5 (volts) / 10000 (ohms) = 0.0005 A, or half a milliamp.

As power dissipated (watts) = voltage x current, power equals 0.0025 watts, easily handled by a common 1/4 watt resistor. Our resistor R1 is called a pull-down resistor as it pulls the voltage at input A down to zero volts.

And with R2, when SW2 is open, input B is connected directly to 5V via R2. However. as the IC inputs are high impedance, the voltage at input B will still be 5V (perfect). When SW2 is closed, input B will be set to zero volts, via the direct connection to ground. Again, some current will flow through the resistor R2, in the same way as R1. However, in this situation, we call R2 a pull-up resistor, as it pulls the voltage at input B up to 5V.

Generally 10k ohm resistors are the norm with CMOS digital circuits like the ones above, so you should always have a good stock of them. If you are using TTL ICs, inputs should still not be left floating, use a pull-up resistor of 10k ohm as well. Pull-up resistors can also be used in other situations, such as maintaining voltages on data bus lines, such as the I2C bus (as used in our Arduino clock tutorials).

In the meanwhile have fun and keep checking into tronixstuff.com. Why not follow things on twitterGoogle+, subscribe  for email updates or RSS using the links on the right-hand column? And join our friendly Google Group – dedicated to the projects and related items on this website. Sign up – it’s free, helpful to each other –  and we can all learn something.

 

Posted in education, learning electronics, lesson, pulldown, pullup, resistor, tutorialComments (12)

Electronic components – the Resistor (Part Two)

Hello readers

Today we continue with the series of articles on basic electronics with this continuation of the article about the resistor. Part one can be found hereWith regards to this article, it is only concerned with direct current (DC) circuits. In this chapter we will examine how two or more resistors alter the flow of current in various ways. First of all, let’s recap what we learned in the previous chapter.

Ohm’s Law – the relationship between voltage, current and resistance:

ohmslaw

Resistors in series:

series

Resistors in parallel:

parallel

 

Dividing voltage with resistors:

divider

However the fun doesn’t stop there. As there is a relationship between voltage, current and resistance, we can also divide current with resistors. For now we will see how this works with two resistors. Please consider the following:

There is a balance between the two resistors with regards to the amount of current each can handle. The sum of the current through both resistors is the total current flowing through the circuit (It). The greater the resistance the less current will flow, and vice versa. That is, they are inversely proportional. And if R1 = R2, I1 = I2. Therefore, I1/I2=R2/R1 – or you can re-arrange the formula to find the other variables.

Here is an example of doing just that:

currdivex2

Our problem here – there is 6 volts DC at half an amp running from left to right, and we want to use an indicator LED in line with the current. However the LED only needs 2 volts at 20mA. What value should the resistors be?

First of all, let’s look at R1. It needs to change 6V to 2V, and only allow 20 mA to pass. R=E/A or R= 4 volts /0.2 amps = 200 ohms.

So R1 is 200 ohms. I1 is .02 A. Now we know that the total current is equal to I1+I2, so I2 will be 0.48A. That leaves us with the known unknown R2 🙂  We can re-arrange the formula R2/R1=I1/I2 to get R2 = (R1 x I1)/I2 – which gives us R2 of 8.3 ohms. Naturally this is a hypothetical, but I hope you now understand the relationship between the current through the resistors, and their actual resistance.

What we have just demonstrated in the problem above is an example of Kirchhoff’s current law (KCL). Gustav Kirchhoff was another amazing German physicist who worked on the understandings of electrical circuits amongst other things. More on GK here. His current law states that the amount of current entering a junction in a circuit must be equal to the sum of the currents leaving that junction. And not-coincidentally, there is also Kirchhoff’s voltage law (KVL) – the amount of voltage supplied to a circuit must equal the sum of the voltage drops in the circuit. These two laws also confirm one of the basic rules of physics – energy can not be created nor destroyed, only changed into different forms.

Here is a final way of wrapping up both KCL and KVL in one example:

The current through R3 is equal to I1 + I2

Therefore, using Ohm’s law, V1 = R1I1 + (R3 x (I1+I2)) and V2 = R2I2 + (R3 x (I1+I2))

So with some basic algebra you can determine various unknowns. If algebra is your unknown, here is a page of links to free mathematics books, or have a poke around BetterWorldBooks.

There is also another way of finding the currents and voltages in a circuit with two or more sources of supply – the Superposition Theorem.

This involves removing all the sources of power (except for one) at a time, then using the rules of series and parallel resistors to calculate the current and voltage drops across the other components in the circuit. Then once you have all the values calculated with respect to each power source, you superimpose them (by adding them together algebraically) to find the voltages and currents when all the power sources are active. It sounds complex, but when you follow this example below, you will find it is quite simple. And a lot easier the th.. fourth time.  Just be methodical and take care with your notes and calculations. So let’s go!

Consider this circuit:

scan1

With the Superposition theorem we can determine the current flowing through the resistors, the voltage drops across them, and the direction in which the current flows. With our example circuit, the first thing to do is replace the 7V power source with a link:

Next, we can determine the current values. We can use Ohm’s law for this. What we have is one power source, and R1 which is in series with R2/R3 (two parallel resistors). The total current in the circuit runs through R1, so calculate this first. It may help to think of the resistors in this way:

Then the formula for Rt is simple (above), and Rt is And now that we have a value for Rt, and the voltage (28V) the current is simple:

scan3

Which gives us a value of 6 amps for It. This current flows through R1, so the current for R1 is also 6 amps. Next, the current through R2:

Using Kirchhoff’s Current Law, the current flowing through R2 and R3 will equal It. So, this is 4 amps.

At this point, note down what we know so far:

For source voltage 28V, Ir1 = 6A, Ir2 = 2A and Ir3 = 4A; R1=4 ohms, R2 = 2 ohms, R3 = 1 ohm.

Now – repeat the process by removing the 28V source and returning the 7V source, that is:

The total resistance Rt:

Gives us Rt = 2.3333 ohms (or 2 1/3);

Total current It will be 7 volts/Rt = 3 amps, so Ir3 = 3;

So Ir2 = 2A – therefore using KCL Ir1 = 3-2 = 1A.

So, with 7V source: Ir1 = 1A, Ir2 = 2A and Ir3 = 3A.

Next, we calculate the voltage drop across each resistor, again by using only one voltage source at a time. Using Ohm’s law, voltage = current x resistance.

For 28V:

Vr1 = 4 x 6 = 24V; Vr2 = 2 x 2 = 4V; Vr3 = 4 x 1 = 4V. Recall that R2 and R3 are in parallel, so the total voltage drop (24 + 4V) = 28 V which is the supply voltage.

Now, for 7V:

Vr1 = 4V, Vr2 = 4V, Vr3 = 3V.

Phew – almost there. Now time to superimpose all the data onto the schematic to map out the current flow and voltage drops when both power sources are in use:

scan11

Finally, we combine the voltage values together, and the current values together. If the arrow is on the left, it is positive; on the right – negative. So:

Current – Ir1 = 6 – 1 = 5A; Ir2 = 2 +2 = 4A; Ir3 = 4-3 = 1A;
Voltage – Vr1 = 24 – 4 = 20V; Vr2 = 4 + 4 = 8V; Vr3 = 4 – 3 = 1V.

And with a deep breath we can proudly show the results of the investigation:

So that is how you use the Superposition theorem. However, there are some things you must take note of:

  • the theorem only works for circuits that can be reduced to series and parallel combinations for each of the power sources
  • only works when the equations are linear (i.e. straight line results, no powers, complex numbers, etc)
  • will not work when resistance changes with temperature, current and so on
  • all components must behave the same way regardless to polarity
  • you cannot calculate power (watts) with this theorem, as it is non-linear.

Well that is enough for today. I hope you understood and can apply what we have discussed today. The final chapter on resistors can be found here. And if you made it this far – check out my new book “Arduino Workshop” from No Starch Press.

In the meanwhile have fun and keep checking into tronixstuff.com. Why not follow things on twitterGoogle+, subscribe  for email updates or RSS using the links on the right-hand column? And join our friendly Google Group – dedicated to the projects and related items on this website. Sign up – it’s free, helpful to each other –  and we can all learn something.

Posted in education, kirchoff, learning electronics, resistorComments (6)


Subscribe via email

Receive notifications of new posts by email.

The Arduino Book

Arduino Workshop

Für unsere deutschen Freunde

Dla naszych polskich przyjaciół ...

Australian Electronics!

Buy and support Silicon Chip - Australia's only Electronics Magazine.

Use of our content…

%d bloggers like this: