The Wheatstone Bridge, by K4ICY

Practical Electronics Projects By Mike, K4ICY

Weekend Radio Click Here for More Electronics Projects and Tutorials By Mike Maynard, K4ICY

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Building Bridges - Yes you can! And find values of mystery capacitors – with your multimeter
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Originally published in The Printed Circuit, Newsletter of the Tallahassee Amateur Radio Society, August 2013, page 14
[VISIT HERE] Edited/Updated December 2023
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The Wheatstone Bridge

It’s hard to fathom – the Wheatstone Bridge circuit has been around for nearly two centuries! Invented by Samuel Hunter Christie in 1833 and improved and popularized by Sir Charles Wheatstone in 1843 [Wiki and citations,] the Wheatstone Bridge and other related configurations are the most fundamental electronics testing applications, still even used today. The bridge is basically a ring of components configured so that each leg (generally two,) of the circuit will electrically balance out each other under test. Once balanced, a measuring device such as a voltmeter can help identify an unknown resistance integrated within the bridge setup. Measurements made by a bridge can be extremely accurate and bridge design variations can be used to also find capacitance, inductance, impedance, and reactance among other quantities.
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Referencing the diagram shown [BELOW], the circuit is made up for four resistances: R1-R4. The “Generator,” (a battery,) is connected across the two outside points of the ring and the “Detector” (a voltmeter) is connected across the remaining points of the ring which are the mid-point connections of each “leg” of the bridge; each composed of R1-R2 and R3-R4. When proper resistances are used within the bridge, no current will flow through the meter and the bridge is said to be “balanced.” For all other combinations of resistances the meter will receive some current and thus deflect to indicate an imbalance within the bridge.
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Of the two legs of the bridge, R1 and R2 are a known and fixed value. R3 is called the “Control,” and a variable resistance, implemented by a potentiometer, is used to find the balance point. R4 is the unknown component under test. This happens to be the same configuration used in many of your electronics test equipment such as multimeters and vector network analyzers to derive resistance values and other electrical attributes under test, and this even applies to modern digital devices. The use of the bridge requires some simple mathematical relationships: balance is obtained when the ratios of each adjacent ring leg resistances are equal. Note the formulas listed in the graphic: R4 divided by R3 is equal to R2 divided by R1. If R4 is the unknown resistance to be measured, you can rearrange the formula to solve for this resistance in terms of the other three known resistances: R4 equals R3 times (R2 divided by R1).

Notice that R1 and R2 are arranged in the form of a ratio in the latter formula. For this reason, each pair of resistances are called the “ratio legs” of the bridge. Consequently, if R1 and R2 are of equal resistance value (a 1:1 ratio,) then when R3 and R4 are equal the bridge will be in balance. So if R4, the mystery component under test, has 33k ohms of resistance, once R3, a 50k ohm potentiometer is turned to 33k of resistance, falling within it's useful range of 50k ohms, that leg will then have a 1:1 ratio of resistance, the bridge will balance and the meter will show no voltage as no difference-current will pass through it.

Are there uses for bridge circuits in Amateur Radio? More than you know. Though, in different configurations such as the “Noise Bridge” which has been used as long as radio itself was around for analyzing and balancing an impedance match within an antenna system. An antenna analyzer uses this method to help match system impedances, indicating what is needed to reduce the unwanted standing wave ratio (SWR) which can be harmful to both the transmitter and operator as radio frequency energy is reflected back. A network vector analyzer, known as a "VNA," uses a more complex arrangement to plot complex impedances and other RF electrical characteristics and is a very useful tool in many of ham shacks. A NanoVNA is a small pocket-sized device which can be had for $50. In the next circuit, we’ll see how a bridge circuit can be used to discover the component values of unmarked mystery capacitors scavenged from discarded electronics!
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A Capacitance Bridge

If you’ve experimented with electronics for some time, no doubt you’ve got a bin or even bags lying somewhere filled with impossible to identify capacitors. Many were probably cannibalized from old televisions and radio gear and often have their markings scratched off or come with odd markings such as dots and stripes that used to be legible, but no more… why throw out good components? "Good" as in ceramic, mica and film capacitors. You should discard most electrolytic, including aluminum and polypropylene types. Certain capacitors can go bad over time due to factors such as age, overvoltage, overheating, or manufacturing defects which can cause devices to fail or even be dangerous to use.

Can't my department store digital multimeter do the trick? Sure, only if they're the more pricey precision ones you may find at the big-box home repair stores. No problem when it comes to resistors and diodes, but most likely, your dollar store automotive department meter doesn’t have a setting for inductors or capacitors. For that ability on a multimeter you’ll be paying at least $100. For only $5 to $30 you can use one of the many Arduino-based "component testers" found on eBay, Amazon, AliExpress and others - and I suggest you do. But I present to you a simple circuit you can practically build with spare transistor radio parts you have laying around for almost nothing! Of course, if you’re getting serious about electronics, one of those nice do-it-all meters spoken of would be a wise investment, and some can tell you more about your capacitors, such as leakage, equivalent series resistance, and integral inductance.
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The purpose of this capacitance bridge circuit here, is to demonstrate a variation of the bridge-measurement concept. You should, after a little calibration and comparison, be able to roughly identify capacitor component values in the range between 1 nano-Farad to 10 micro-Farads. This circuit uses the same fundamental bridge concept used by more expensive meters, but for more accuracy and the ability to test a broader range of components such as the ‘pico-Farad’ values, other circuits employing IC-derived timing and other schemes can be had as kits or for homebrew construction for as low as $15. For the sake of learning, go ahead and put this one on your ‘try’ list anyways.
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Circuit Description:

This circuit is a basic common pulse-type audio oscillator combined with a modification of the Wheatstone Bridge and involves substituting capacitors for the top portion of the adjacent legs of the bridge and then using a 10k ohm potentiometer for the bottom portion. Any PNP transistor can be used and the audio signal matching transformer should be a 1k ohm : 8 ohm type with a center tap on the 1k side. These used to be sold by Radio Shack as part no.: 273-1380, but it is best now to just search around online. The 1k is not critical, 500 ohm or 2000 ohm will work fine as long as there is a workable ratio. Amazon and eBay are good starts, but I'm sorry to say that they aren't as easy to find for cheap these days since the demise of Radio Shack, and let us also consider the preferred used of class-D PWM chip-based amplifiers in most contemporary electronics goods. There are many options online but just stop short of paying more than $15 for one. The only external accessories will be any pair of headphones or crystal ear-buds and your multimeter which must be capable of reading millivolts of alternating current (mV AC).
The meter is not a requirement as described later, as you'll be able to play this "by ear."
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Capacitance Bridge on a Solderless Breadboard

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The bridge functions just as its resistance variation, but in this case, an audio AC current signal is induced across the secondary windings of the transformer. R2, the 10k ohm pot, distributes current at different levels to each capacitor; one known and the other one unknown, thus affecting the charging time and phase rate of each capacitor/resistor combination. When balanced, of course, no current flows across the headphone coils and the audio signal is at its lowest level, or essentially shut off. Adversely, when in its balanced state, this particular bridge configuration causes more current to flow through the meter as the phasing of the audio signal, or lack thereof, is not present to be applied to the headphones and you get a 'null' in the tone. The use of the meter, though useful, is not necessary as the audio is an approximate indicator itself.
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Circuit Operation:

[Referencing the ABOVE circuit diagram] 1. Connect unknown value capacitor at ‘Cx’. 2. Push the button to supply power to the oscillator. You should be hearing a tone. It might also sound raspy if it is overdriven. If it is not heard, adjust the control knob. 3. Adjust the 10k ohm potentiometer for minimum audio volume in the headphones, or note the highest voltage reading on your meter. This is when the bridge is in balance. 4. Compare your control dial setting with settings or voltage readings obtained by measuring capacitors of known value. It is suggested that you use a regulated power supply so that you get consistent readings later on. For the calibration process, take many known value components within the full range and note their result settings, including meter readings, on a simple chart. If the test falls to one end of your calibration scale or the other, then it’s most likely either a ‘pico’-valued capacitor or a higher micro-Farad type. You may also notice that the volume will increase in proportion to higher capacitance values. This is due to the ‘charge-pump’ effect. So, once you plug-in and test that mystery capacitor with the strange multi-colored identification dots, you should have a really good idea on its general value. Though not a concise test, it should be an interesting academic exercise.
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The weekend is here, so go and build something!
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73! DE Mike, K4ICY MikeK4ICY@gmail.com