2014-02-10T19:57

2014-02-10T19:57

Audiophile's Software

PROLOGUE A: The headphone output impedance is one of the most common reasons why the same headphones can sound different depending on where they are plugged into. This important parameter is rarely specified by manufacturers, but at the same time, it can cause significant differences in sound quality and greatly affect headphone compatibility.

SUMMARY: All you really need to know is that most headphones work best when the output impedance of the device is less than 1/8 of the headphone impedance. So, for example, for 32 ohm Grados, the output impedance should be a maximum of 32/8 = 4 ohms. The Etymotic HF5 is 16 ohms so the maximum output impedance should be 16/8 = 2 ohms. If you want to be sure that the source will work with any headphones, make sure its output impedance is less than 2 ohms.

WHY IS OUTPUT IMPEDANCE SO IMPORTANT? For at least three reasons:

• The larger the output impedance, the greater the voltage drop at lower load impedances. This drop can be large enough to prevent low-impedance headphones from "swinging" to the desired volume level. An example is the Behringer UCA202 with an output impedance of 50 ohms. It loses a lot in quality when using 16 - 32-ohm headphones.
• Headphone impedance varies with frequency. If the output impedance is much greater than zero, this means that the voltage dropped across the headphones will also change with frequency. The greater the output impedance, the greater the frequency response flatness. Different headphones will interact differently (and usually unpredictably) with different sources. Sometimes these differences can be significant and quite audible.
• As the output impedance increases, the damping factor decreases. The level of bass, which was calculated for headphones during design, can be significantly reduced with insufficient damping. Low frequencies will be more buzzing and not as clear (smeared). The transient response deteriorates, and the depth of the bass suffers (more roll-off at low frequencies). Some people, like those who like the "warm tube sound", may even find this underdamped bass to their liking. But in the vast majority of cases, this gives a less honest sound than when using a low-impedance source.

RULE OF ONE EIGHTH: To minimize each of the above effects, it is only necessary to ensure the output impedance is at least 8 times lower than the headphone impedance. Even simpler: Divide the headphone impedance by 8 to get the maximum amplifier impedance to avoid audible distortion.

IS THERE ANY STANDARD FOR OUTPUT IMPEDANCE? The only such standard that I know of is IEC 61938 (1996). It sets the output impedance requirement to 120 ohms. There are several reasons why these requirements are outdated and generally not a good idea. The Stereophile article on the standard value of 120 ohms literally says the following:

"Whoever wrote this is clearly living in a dream world"

I must agree. Perhaps a value of 120 ohms was still acceptable (and then hardly) before the advent of the iPod and before portable devices generally gained wide popularity, but no more. Today, most headphones are designed completely differently.

PSEUDO STANDARDS: The headphone outputs of most professional setups are 20 to 50 ohms impedance. I don't know of any that fit 120 ohms like the IEC standard. For consumer grade equipment, the output impedance is typically in the range of 0 to 20 ohms. With the exception of some tube and other esoteric designs, most high-end audiophile equipment has impedances below 2 ohms.

iPOD IMPACT: Ever since the 120-ohm standard was published in 1996, from low-end cassette players, through portable CD players, we've finally moved on to the iPod craze. Apple helped make high quality portable, and now we have at least half a billion digital players, not counting phones Virtually all portable music/media players are powered by single rechargeable lithium-ion batteries These batteries generate a voltage of just over 3 volts, which typically produces about 1 volt (RMS) at the headphone output ( sometimes less.) If you put a 120 ohm output impedance and use regular portable headphones (which are in the range of 16 - 32 ohms), the playback volume will probably not be enough. In addition, most of the battery energy will be dissipated as heat at 120 -ohm resistor.Only a small fraction of the power will go to the headphones.This is a serious problem for portable devices, where it is very important to prolong battery life. It would be more efficient to supply all the power to the headphones.

HEADPHONE DESIGN: So what output impedance do manufacturers design their headphones for? As of 2009, over 220 million iPods have been sold. iPods and similar portable players are like 800-pound gorillas in the headphone market. So it's not surprising that most designers have begun to design headphones in such a way that they are well compatible with the iPod. This means that they are designed to work with an output impedance of less than 10 ohms.And almost all high-end full-size headphones are designed for sources that respect the 1/8 rule, or have an impedance close to zero.I have never seen an audiophile headphones designed for home uses designed according to the ancient 120 ohm standard.

BEST HEADPHONES FOR BEST SOURCES: If you take a quick look at the most over-the-top high-end headphone amplifiers and DACs, you will find that almost all of them have very low output impedance. Examples are Grace Designs, Benchmark Media, HeadAmp, HeadRoom, Violectric, etc. Of course that most high-end headphones perform best when paired with the same class of equipment.Some of the most well-received headphones are inherently low impedance, including various models from Denon, AKG, Etymotic, Ultimate Ears, Westone, HiFiMAN and Audeze. All of them, to my knowledge, were designed for use with a low (ideally zero) impedance source, and a Sennheiser representative told me that they design their audiophile and portable headphones for zero impedance sources.

AFC QUESTION: If the output impedance is greater than 1/8 of the headphone impedance, there will be a flat frequency response. For some headphones, especially armature (balanced armature) or multi-driver headphones, these differences can be enormous. Here's how 43 ohms of output impedance affects the Ultimate Ears SuperFi 5's frequency response - a palpable 12 dB flatness:

OUTPUT IMPEDANCE 10 ohms: Some may look at the example above and think that such a significant difference only appears at 43 ohms. But many sources have an impedance of about 10 ohms. Here are the same headphones with a 10 ohm source - still audible 6 dB unevenness. Such a curve results in weak bass, pronounced mid-range emphasis, muffled highs, and unclear phase response due to a sharp 10 kHz dip, which can affect stereo imaging.

FULL SIZE SENNHEISER: Here are the full-sized, higher-impedance Sennheiser HD590s with the same 10-ohm source. Now the ripple above 20 Hz is only a little over 1 dB. Although 1 dB is not that much, the unevenness is in the area of ​​"humming" bottoms, where any accent is highly undesirable:

HOW DAMPING WORKS: any speaker head, be it headphones or speakers, moves back and forth as music plays. Thus, they create sound vibrations, representing a moving mass. The laws of physics state that a moving object tends to stay in motion (i.e. has inertia). Damping also helps to avoid unwanted movements. Without going into too much detail, an underdamped speaker continues to move when it should have stopped. If the speaker is overdamped (which rarely happens), its ability to move according to the applied signal is limited - imagine that the speaker is trying to work immersed in maple syrup. There are two ways to dampen a speaker - mechanical and electrical.

JUMPING CARS: Mechanical damping is similar to the shock absorbers in a car. They add resistance, so if you rock the car, it won't bob up and down for a long time. But cushioning also adds stiffness, because it doesn't allow the suspension to change its position in full accordance with the road surface. Therefore, a compromise has to be found here: soft shock absorbers make the ride softer, but lead to swaying, while hard ones make the ride less comfortable, but prevent swaying. Mechanical damping is always a compromise.

ELECTRIC PERFECT: There's a better way to control unwanted diffuser movement, it's called electrical damping. Coil and magnet interact in dynamics with amplifier to control the movement of the diffuser. This type of damping has fewer side effects and allows designers to create headphones with less distortion and better sound. Like a car's suspension that can more accurately adjust to the road, optimally damped headphones can reproduce the audio signal more accurately. But, and this is the critical moment, electrical damping is only effective when the output impedance of the amplifier is much less than the headphone impedance . If you plug 16 ohm headphones into an amplifier with a 50 ohm output impedance, the electrical damping disappears. This means that the speaker will not stop when it should stop. It's like a car with worn shock absorbers. Of course, if the 1/8 rule is followed, electrical damping will be sufficient.

ACOUSTIC SUSPENSION: In the 70s, the situation changed, as transistor amplifiers became popular. Almost all transistor amplifiers follow the 1/8 rule. In fact, most conform to the 1/50 rule - their output impedance is less than 0.16 ohms, which gives a damping factor of 50. In this way, speaker manufacturers have been able to design better speakers that take advantage of the low output impedance. First of all, the first closed acoustically suspended speakers from Acoustic Research, Large Advents, and others were developed. They had a deeper and more accurate bass than similarly sized predecessors designed for tube amplifiers. This was a big breakthrough in hi-fi, thanks to the new amplifiers you could now rely heavily on electrical damping. And it is a pity that so many sources today are 40 or more years behind the times.

WHAT IS THE OUTPUT IMPEDANCE OF MY DEVICE? Some developers make it clear that they aim to keep the output impedance as low as possible (like the Benchmark), while others list the actual value for their products (like 50 ohms for the Behringer UCA202). Most, unfortunately, leave this meaning a mystery. Some hardware reviews (such as the one on this blog) include measuring the output impedance, as this is a big factor in how a device will sound with certain headphones.

WHY DO SO MANY SOURCES HAVE HIGH OUTPUT IMPEDANCE? The most common reasons are:

• Headphone protection- Higher power sources with low output impedance are often able to deliver too much power to low impedance headphones. To protect these headphones from damage, some designers increase the output impedance. So this is a trade-off that adapts the amplifier to the load, but at the cost of performance degradation for most headphones.. The best solution is the ability to select two gain levels. A low level allows you to set a lower output voltage for low impedance headphones. Also, current limiting can be used in addition, so the source will automatically limit the current for low-impedance headphones, even if the gain level is set too high.
• To be different- Some developers deliberately increase the output impedance, claiming that this improves the sound of their device. This is sometimes used as a way to make a product sound different from competing products. But in that case, every "single sound" you get depends entirely on the headphones you're using. For some headphones, this is perceived as an improvement, while for others it is rather a significant deterioration. It is most likely that the sound will be significantly distorted.
• It is cheap- Higher output impedance is the simplest solution for low cost sources. This is a cheap way to achieve stability, the simplest short circuit protection; it also allows the use of lower quality op amps that even 16 or 32 ohm headphones would otherwise not drive directly. By connecting some resistance in series to the output, all these problems are solved at a price of some cent. But for this cheap solution, you have to pay a significant deterioration in sound quality on many headphone models.

EXCEPTIONS TO THE RULES: There are several headphones purportedly designed for high output impedance use. Personally, I wonder if this is a myth or reality, since I do not know of any specific example. However, it is possible. In this case, the use of these headphones with a low-impedance source may lead to overdamped bass dynamics and, as a result, to a frequency response different from the designer's intended one. This may explain some cases of "synergy", when certain headphones are combined with a certain source. But this effect is perceived purely subjectively - for someone as expressiveness and detail of sound, for someone - as excessive rigidity. The only way to achieve adequate performance is to use a low-resistance source and follow the 1/8 rule.

HOW TO CHECK IT INEXPENSIVELY: If you are wondering if the sound quality suffers due to the output impedance of the source, I can suggest buying the FiiO E5 amplifier for $19. It features a near-zero impedance output and will be sufficient for most impedance headphones.

TOTAL: Unless you're absolutely sure that your headphones sound better with some particular higher output impedance, it's best to always use sources with an impedance no greater than 1/8 of your headphones' impedance. Or even simpler: with an impedance of no more than 2 ohms.

TECHNICAL PART

IMPEDANCE AND RESISTANCE: The two terms are interchangeable in some cases, but technically they have significant differences. Electrical resistance is denoted by the letter R and has the same value for all frequencies. Electrical impedance is a more complex quantity, and its value usually changes with frequency. It is marked with beech Z. Within the framework of this article, the units of measurement for both quantities are Ohms.

VOLTAGE AND CURRENT: To understand what impedance is, and what this article is all about, it is important to have at least a general idea of ​​​​voltage and current. Voltage is similar to water pressure, while current is analogous to water flow (eg liters per minute). If you run water from your garden hose without attaching anything to the end of the hose, you will get a lot of water flow (current) and you can quickly fill a bucket, but the pressure near the end of the hose will be practically zero. If you use a small nozzle on the hose, the pressure (tension) will be much greater, and the flow of water will decrease (it will take more time to fill the same bucket). These two values ​​are inversely related. The relationship between voltage, current, and resistance (and impedance, for the purposes of this article) is defined by Ohm's Law. R can be replaced by Z.

WHERE DID THE 1/8 RULE COME FROM?: The minimum audible difference in loudness that is perceived by a person is about 1 dB. A -1 dB drop in the output impedance corresponds to a factor, 10^(-1/20) = 0.89 . Using the voltage divider formula, we get that when the output impedance is 1/8 of the load impedance, the ratio is exactly 0.89, i.e., the voltage drop is -1 dB. Headphone impedance can vary within the audio band by a factor of 10 or more. For SuperFi 5, the impedance is 21 ohms, but in fact it varies from 10 to 90 ohms. So the 1/8 rule gives us a maximum output impedance of 2.6 ohms. If we take the source voltage equal to 1 V:

• Headphone voltage at 21 ohm impedance (nominal) = 21 / (21+2.6) = 0.89 V
• Headphone voltage at 10 ohm impedance (minimum) = 10 / (10+2.6) = 0.79 V
• Headphone voltage at 90 ohm impedance (maximum) = 90 / (90+2.6) = 0.97 V
• Frequency response flatness = 20*log(0.97/0.89) = 0.75 dB (less than 1 dB)

OUTPUT IMPEDANCE MEASUREMENT: As you can see from the circuit diagram above, the output impedance forms a voltage divider. By measuring the output voltage with no load connected and with a known load, you can calculate the output impedance. This can be easily done with an online calculator. The no-load voltage is "Input Voltage", R2 is the known load resistance (do not use headphones in this case), "Output Voltage" is the voltage when the load is connected. Press Compute and get the desired output impedance R1. You can also do this with a 60 hertz sine wave (you can generate it, for example, in Audacity), a digital multimeter and a 15 - 33 ohm resistor. Most DMMs only have good accuracy around 60 Hz. Play a 60 Hz sine wave and adjust the volume so that the output voltage is approximately 0.5 V. Then connect a resistor and note the new voltage value. For example, if you get 0.5V with no load and 0.38V with a 33 ohm load, the output impedance is about 10 ohms. The formula here is as follows: Zist = (Rн * (Vхх - Vн)) / Vн. Vxx - voltage without load (idle).

No headphones have a completely resistive impedance that does not change over the audio frequency range. The vast majority of headphones are reactance and have a complex impedance. Due to the capacitive and inductive components of headphone impedance, its value changes with frequency. For example, here is the dependence of impedance (yellow) and phase (white) on frequency for Super Fi 5. Below ~200 Hz, the impedance is only 21 ohms. Above 200 Hz it rises to ~90 ohms at 1200 Hz and then drops to 10 ohms at 10 kHz:

FULL SIZE HEADPHONES: Perhaps someone is not interested in in-ear headphones like the Super Fi 5, so here are the impedance and phase for the popular Sennheiser HD590 model. The impedance still varies: from 95 to 200 ohms - almost twice:

MATTER: One of the graphs at the beginning of the article showed about 12 dB of frequency response ripple for SuperFi 5 connected to a source with an impedance of 43 ohms. If we take the nominal value of 21 ohms as a reference, and take the output voltage of the source equal to 1 V, the voltage level at the headphones will be as follows:

• Reference level: 21 / (43 + 21) = 0.33 V - which corresponds to 0 dB
• At a minimum impedance of 9 ohms: 9 / (9 + 43) = 0.17 V = -5.6 dB
• At a maximum impedance of 90 ohms: 90 / (90 + 43) = 0.68 V = +6.2 dB
• Range = 6.2 + 5.6 = 11.8 dB

DAMPING LEVELS: Speaker damping, as explained earlier, can be either purely mechanical (Qms) or a combination of electrical (Qes) and mechanical damping. The total damping is denoted by Qts. How these parameters interact at low frequencies is explained by Thiel-Small modeling. Damping levels can be divided into three categories:

• Critical Damping (Qts = 0.7) - Considered by many to be the ideal case, as it delivers the deepest bass without any frequency response deviation or excessive ringing (uncontrolled cone movements). The bass of such a speaker is usually perceived as "resilient", "clear" and "transparent". Most people think that Qts 0.7 provides ideal transient response.
• Excess damping (Qts
• Weak Damping (Qts > 0.7) - Allows for some bass boost with a peak at the top of the bass range. The speaker is not fully controlled, resulting in excessive "ringing" (i.e., the cone does not stop moving fast enough after the electrical signal is attenuated). Weak damping leads to frequency response deviations, less deep bass, poor transient response and rise in the frequency response in the region of the upper limit of the bass. Weak damping is a cheap way to boost bass at the cost of bass quality. This technique is actively used in cheap headphones in order to create "fake bass". The sound of underdamped speakers is often characterized as "boomy" or "sloppy" bass. If your headphones are designed for electrical damping, and you use them with a source that has an impedance greater than 1/8 of the headphone impedance, you will get just that, underdamped bass. .

DAMPING TYPES: There are three ways to dampen speakers / control resonance:

• Electrical damping- Already known to us Qes, it is similar to regenerative braking in hybrid electric vehicles. When you apply the brakes, the electric motor slows down the car, turning into a generator and transferring energy back to the batteries. The speaker is capable of doing the same. But if the output impedance of the amplifier is increased, the braking effect is significantly reduced - hence the 1/8 rule.
• Mechanical damping- Known as Qms, it is rather similar to car shock absorbers. As you increase the mechanical damping of a speaker, it limits the music signal that drives it, resulting in more non-linearity. This increases distortion and reduces sound quality.
• Damping due to the housing- The enclosure can provide damping, but it requires it to be closed - either with a properly tuned bass reflex or controlled clipping. Many top-end headphones are, of course, open, which eliminates the possibility of using case damping, as in loudspeakers.

PRESS LEVEL: For headphones that have a reasonably snug fit, such as full-size ear cups with tight-fitting ear cups, designers may consider allowing for some additional cushioning from the earcup. But the shape of the head, ears, hairstyle, fit of the headphones, the presence of glasses and other factors make this effect almost unpredictable. For on-ear headphones, this feature is not available at all. Below you see two graphs depicting the impedance of the Sennheiser HD650. Please note: the resonant peak at the open bass is 530 ohms, but when using an artificial head, the value drops to 500 ohms. The reason for this is the damping due to the closed space formed by the auricle and the ear cups.

CONCLUSION: I hope it's now clear that the only way to achieve efficient headphone-amp performance is to follow the 1/8 rule. While some people prefer the sound of a higher output impedance, it is highly dependent on the headphone model used, the value of the output impedance, and personal preference. Ideally, a new standard should be created, according to which developers would have to produce sources with an output impedance of less than 2 ohms.

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Original article in English: Headphone & Amp Impedance

Why is the value of the output impedance of the source (amplifier) ​​so important, how does it interact with the headphones and what does it affect.

Copyright Taras Kovrijenko 2009–2019

I think many people know that if you turn on the high beam, stove, heated rear window on a running car, then the voltage generated by the generator will decrease, even in this case they say that the voltage has subsided. How does this apply to electronics? In electronics, everything happens according to the same scenario, if you connect some low-resistance load to the signal generator, then the voltage at its terminals will decrease, the reason for this in both cases is the internal resistance of the generator, which is usually depicted as a resistor connected in series with the generator. Generator Equivalent Circuit shown in the picture below.

Why equivalent? Because in fact, physically, the resistor shown in the picture is not, at least, in the car generator, but in order to take into account the processes occurring inside the generator or amplifier, as well as in other circuits, it is convenient to describe them in this way.
Let's move on to practice, we will measure the output impedance of the signal generator.
First, connect the oscilloscope to the outputs of the signal generator as shown in the picture below and see what the voltage will be.

The oscillogram shows that the amplitude value of the voltage is 1 V.
Now let's connect a potentiometer to the outputs of the signal generator and turn it until the voltage at the ends of the generator becomes equal to half of the previously measured one, that is, 0.5 V.

With a resistance of 51 Ohm, the voltage drop across the potentiometer became equal to half the open circuit voltage.
If you look at the picture above, you can see that the internal resistance of the generator and the potentiometer connected by us form a voltage divider and the voltage drop on one of its arms is equal to half the voltage of the generator, which means that exactly half of the voltage remains on the second arm. Since the voltage drops on the internal resistance and on the potentiometer connected by us are equal, this means that the internal resistance of the generator is equal to the resistance of the potentiometer, that is, 51 Ohm.
But there are times when it is not possible to measure the voltage of the generator at idle, that is, without load, in which case two measurements are made with different resistances and the generator resistance is calculated using the formula shown below.

The formula is derived as follows, first the voltage across R1 and R2 is calculated, just like a conventional divider. In both formulas obtained, the generator voltage will be present, we express it from each formula and equate the other parts. Next, you just need to express Rg and this completes the calculation.
Now we know how to measure the output impedance of the generator.

6.3. Installation and study of an aperiodic low-frequency amplifier on a bipolar transistor

In bipo ampsIn polar transistors, three transistor connection schemes are used: with a common base, with a common emitter, with a common collector. The most widely used switching circuit with a common emitter.

Recall that the input circuits of a sensitive low-frequency amplifier are necessarily performed with a shielded wire.

To study the operation of the amplifier according to the diagram of the figure 6.6 you can assemble the amplifier using the one shown in the figure 6.8 mounting board.

When mounting the amplifier, it is imperative to observe the polarity of the connection of electrolytic capacitors. The wiring diagram shows the polarity of connecting only one electrolytic capacitor. The polarity of connecting the other two capacitors is determined by the circuit diagram of the amplifier. Since the output of the generator is sinusoidsIf there is no direct voltage component, then the polarity of the capacitors when using n-p-n type transistors should be as shown in Figure 6.6, and for a p-n-p type transistor - in Figure 6.7.

Since electrolytic capacitors have inductive resistance, in high-quality low-frequency amplifiers, small ceramic capacitors are placed in parallel with electrolytic capacitors.

Measuring sensitivity and rated output

low frequency amplifier power

Preliminarily set the required value of the harmonic coefficient at the output of the amplifier. The amplifier volume control is set to the maximum volume position, and the tone controls to the middle position. Connect all measuring instruments to the network devices and supply voltage to the amplifier. A sinusoidal voltage with a frequency of 1000 Hz is supplied from the sound generator through a voltage divider across resistors R 1 , R 2 to the input of the amplifier. Gradually increase the sinusoidal voltage at the input of the amplifier and at the same time measure the harmonic content of the signal at the output of the amplifier. As soon as the harmonic coefficient reaches a predetermined value, the voltage at the output of the amplifier U N.OUT is measured and the voltage at the input of the amplifier U N.IN is determined. If there is no sensitive electronic voltmeter, then the voltage at the input of the amplifier is determined after measuring the voltage with an electronic voltmeter 1 U 1 at the input of the voltage divider (on resistors R 1 and R 2 - fig. 6.9 ).

(6.1)

With a low sensitivity of the amplifier, a voltage divider can be dispensed with, since the interfering voltages that arise when test leads are connected to the input circuit of the amplifier will not significantly affect the measurement results.

The input voltage U n.in characterizes the sensitivity of the amplifier at a given harmonic coefficient at the output of the amplifier. The rated output power at the load R n is determined by the formula:

(6.2)

Harmonic distortion of 5-8% can be approximately determined using an oscilloscope. With this harmonic distortion, the distortion of the sinusoid is noticeable on the oscilloscope screen. It is easier to detect sinusoid distortion if you use a dual-beam oscilloscope and compare the signal at the output of the amplifier with the signal at the input.

Thus, it is possible to measure the sensitivity and determine the rated output power of a low-frequency amplifier with a harmonic coefficient of the signal at the amplifier output of 5-8%, approximately without a harmonic coefficient meter. The maximum output power of the amplifier is determined at a harmonic distortion of 10%.

Measuring the input impedance of an amplifier

The input impedance of a low frequency amplifier is usually measured at 1000 Hz. If the input impedance of the amplifier R in is much less than the internal resistance of the voltmeter used, then to determine the input resistance of the amplifier, a resistor is connected in series with its input, the resistance of which is approximately equal to the input resistance of the amplifier. Two electronic voltmeters are connected as shown in the figure. 6.10 , where R in is the input impedance of the amplifier. Determining the input resistance of the amplifier is reduced to solving the following problem: known voltages U 1 and U 2 shown by voltmeters V 1 and V 2, the resistance of the resistor R; it is required to determine R in. Since the internal resistance of the voltmeter V 2 is much greater than the input resistance of the amplifier, then:

(6.3)

If the input resistance of the amplifier turns out to be commensurate with the internal resistance of the voltmeter, then it is impossible to determine R in this way.

In this case, to determine the input impedance of the amplifier, devices are assembled according to the diagram of the figure 6.9 , but only without a harmonic coefficient meter. A sinusoidal voltage with a frequency of 1000 Hz is applied to the input of the amplifier, not exceeding the nominal input voltage. The input U in1 and output U out1 of the amplifier voltage are measured and the voltage gain K = U out1 / U in1 is determined. Then, resistor R is connected in series with the input of the amplifier and, without changing the voltage at the output of the sound generator, the voltage at the output of the amplifier Uout2 is measured. The voltage at the output of the amplifier has decreased, since when the resistor R is connected in serieswith the input of the amplifier, part of the voltage from the output of the generator falls on the resistor R, and part - on the input resistance R in. Based on the laws of serial connection, we can write:

U in1 = U R + U R in (6.4)

(6.5)

We express U Rin and Uin1 in terms of the voltage at the output of the amplifier

(6.6) (6.7)

Substituting (6.6) and (6.7) into (6.5) we get:

(6.8)

From (6.8) we obtain an expression for the input impedance of the amplifier:

(6.9)

To improve the accuracy of determining Rin, it is necessary that the resistance of the resistor R be of the same order with the input impedance of the amplifier R in.

Amplifier Output Impedance Measurement

The output impedance of the amplifier is determined from Ohm's law for a complete circuit

(6.10)

where R n is the load resistance, R ext is the internal (output) resistance of the source. Given that the voltage at the source terminals U = I× R n from (6.10) we get

U=e- I× R ext (6.11)

Turn off R n, then the current I will be very small, therefore, the voltage at the source terminals U will be equal to the electromotive force e. Let's connect R n. Then the voltage drop inside the source (e- U Rн) will refer to the voltage drop across the load U Rн as the internal resistance of the source refers to the load resistance

(6.12) (6.13)

For a more accurate determination of the internal (output) resistance of the amplifier, it is necessary to take the resistance R n of the same order as the internal one.

The output impedance of the amplifier is usually measured at a frequency of 1000 Hz. From the sound generator, a sinusoidal voltage of 1000 Hz is applied to the input of the amplifier,so that when the load is disconnected, the harmonic coefficient of the signal at the output of the amplifier did not exceed the specified for thisvalue amplifier.

To determine the output resistance Rout, measure the output voltage of the amplifier twice. With the load disconnected, the output voltage will be equal to the EMF, and with the connected load - U Rn.

The output impedance of the amplifier is determined by the formula

(6.14)

Building an amplitude characteristic

Important information about the quality of the amplifier can be obtained from the amplitude characteristic. To remove the amplitude characteristics, the devices are assembled according to the scheme of Fig. 6.9 , excluding the harmonic meter. A sinusoidal voltage with a frequency of 1000 Hz is supplied from the sound generator to the input of the amplifier so that the difference between the signal at the output of the amplifier and the sinusoidal becomes noticeable. The obtained value of the input voltage is increased by about 1.5 times and the output voltage of the amplifier is measured with an electronic voltmeter. The obtained values ​​of the input and output voltage of the amplifier will give one of the points (extreme) of the amplitude characteristic of the amplifier. Then, by reducing the input voltage, the dependence of the output voltage on the input is removed. From the amplitude characteristic of the amplifier, the voltage gain is easily determined K \u003d U out / U in. The input and output voltages of the amplifier to determine the gain must be selected on the linear section of the amplitude characteristic. In this case, the gain of the amplifier will not depend on the input voltage.

Amplifier noise floor measurement

D To determine the level of intrinsic noise of the amplifier, the output voltage of the amplifier is measured by connecting a resistor to the input of the amplifier, the resistance of which is equal to the input resistance of the amplifier. The amplifier's own noise level is expressed in decibels - formula (5.6). To reduce the effect of interference from external electromagnetic fields, the input circuits of the amplifier are carefully shielded.

Determination of the efficiency of the amplifier

The efficiency of the amplifier is determined when a sinusoidal voltage with a frequency of 1000 Hz is applied to the input, corresponding to the rated output power. Determine the rated output power according to the formula (6.2)

The power consumed by the amplifier from sources (source) is determined by the formula P 0 =I× U , where I is the current consumed from the source, U is the voltage at the amplifier terminals intended for connecting the power source (the connection diagram of the ammeter and voltmeter is chosen taking into account the minimum error in determining the power consumed by the amplifier, depending on the available ammeter and voltmeter).

Determining the range of amplified frequencies

To determine the range of amplified frequencies and the frequency distortion factor, a frequency (amplitude-frequency) characteristic is built.

From the definition of the amplitude-frequency characteristic of the amplifier, it follows that in order to build it, any voltage can be applied to the input of the amplifier, corresponding to the linear section of the amplitude characteristic. However, at too low input voltages, errors due to noise and AC hum may occur. At high input voltages, nonlinearities of the amplifier elements may appear. Therefore, the frequency response is usually taken at an input voltage corresponding to an output power equal to 0.1 of the nominal.

Devices for taking the amplitude-frequency characteristics are assembled according to the scheme of fig. 6.9 , and the harmonic meter and oscilloscope can not be connected.

The range of amplified frequencies is determined from the amplitude-frequency characteristic, taking into account the allowable frequency distortion. The frequency response of an amplifier is the dependence of the voltage gain on frequency. From fig. 5.5 it can be seen how to determine the range of frequencies amplified by the amplifier (bandwidth) with a decrease in the gain at the cutoff frequencies to 0.7 from the maximum, which corresponds to a frequency distortion factor of 3 dB.

(ABOUT THE REDUCTION OF INTERMODULATION DISTORTIONS AND SOUNDS IN LOUDSPEAKERS)

The difference in the sound of loudspeakers when working with different UMZCHs is primarily noticed by comparing tube and transistor amplifiers: the spectrum of their harmonic distortion is often significantly different. Sometimes there are noticeable differences among amplifiers of the same group. For example, in one of the audio magazines, the ratings given by 12 and 50 W tube UMZCHs tended in favor of a less powerful one. Or was the assessment biased?

It seems to us that the author of the article convincingly explains one of the mystical reasons for the occurrence of transient and intermodulation distortions in loudspeakers, which create a noticeable difference in sound when working with various UMZCH. It also offers affordable methods to significantly reduce the distortion of loudspeakers, which are quite simply implemented using modern element base.

It is now generally accepted that one of the requirements for a power amplifier is to ensure that its output voltage remains unchanged when the load resistance changes. In other words, the output resistance of the UMZCH should be small compared to the load one, amounting to no more than 1 / 10.1 / 1000 of the resistance module (impedance) of the load |Z n |. This view is reflected in numerous standards and recommendations, as well as in the literature. Even such a parameter as the damping coefficient - K d (or damping factor) is specially introduced, equal to the ratio of the nominal load resistance to the output impedance of the amplifier R out PA. So, with a nominal load impedance of 4 ohms and an amplifier output impedance of 0.05 ohms, K d will be 80. The current standards for HiFi equipment require that the damping factor for high-quality amplifiers be at least 20 (and it is recommended not less than 100). For most transistor amplifiers on the market, K d is greater than 200.
The arguments in favor of a small Rout PA (and a correspondingly high Kd) are well-known: these are the interchangeability of amplifiers and loudspeakers, obtaining effective and predictable damping of the main (low-frequency) loudspeaker resonance, as well as the convenience of measuring and comparing the characteristics of amplifiers. However, despite the legitimacy and validity of the above considerations, the conclusion about the need for such a ratio, according to the author, fundamentally wrong!

The thing is that this conclusion is made without taking into account the physics of the work of electrodynamic loudspeaker heads (GG). The vast majority of amplifier designers sincerely believe that all that is required of them is to deliver the required voltage at a given load resistance with as little distortion as possible. Loudspeaker designers, for their part, seem to assume that their products will be powered by amplifiers with negligible output impedance. It would seem that everything is simple and clear - what questions can there be?

Nevertheless, there are questions, and very serious ones. Chief among them is the question of the magnitude intermodulation distortion introduced by the GG when it is operated from an amplifier with negligible internal resistance (voltage source or EMF source).

“What does the output impedance of the amplifier have to do with this? Don't fool me!" the reader will say. - And he's wrong. It has, and the most direct, despite the fact that the fact of this dependence is mentioned extremely rarely. In any case, no modern works have been found that would consider this effect on all parameters of the end-to-end electro-acoustic path - from the voltage at the amplifier input to the sound vibrations. For some reason, when considering this topic, we were previously limited to analyzing the behavior of the GG near the main resonance at low frequencies, while no less interesting things happen at noticeably higher frequencies - a couple of octaves above the resonant frequency.

This article is intended to fill this gap. It must be said that in order to increase accessibility, the presentation is very simplified and schematized, so a number of “subtle” issues remained unconsidered. So, in order to understand how the output impedance of the UMZCH affects intermodulation distortion in loudspeakers, we must remember what the physics of sound radiation from a GG cone is.

Below the main resonance frequency, when a sinusoidal signal voltage is applied to the winding of the GG voice coil, the displacement amplitude of its diffuser is determined by the elastic resistance of the suspension (or air compressed in a closed box) and is almost independent of the signal frequency. The operation of the GG in this mode is characterized by large distortions and a very low output of a useful acoustic signal (very low efficiency).

At the fundamental resonance frequency, the mass of the diffuser, together with the oscillating mass of air and the elasticity of the suspension, form an oscillatory system similar to a weight on a spring. The efficiency of radiation in this frequency range is close to the maximum for this HG.

Above the main resonance frequency, the inertia forces of the diffuser, together with the oscillating air mass, turn out to be greater than the elastic forces of the suspension, so the diffuser displacement is inversely proportional to the square of the frequency. However, the acceleration of the cone in this case does not theoretically depend on the frequency, which ensures the uniformity of the frequency response in terms of sound pressure. Therefore, to ensure the uniformity of the frequency response of the HG at frequencies above the main resonance frequency, a force of constant amplitude must be applied to the diffuser from the side of the voice coil, as follows from Newton's second law (F=m*a).

The force acting on the cone from the voice coil is proportional to the current in it. When the GG is connected to a voltage source U, the current I in the voice coil at each frequency is determined from Ohm's law I (f) \u003d U / Z g (f), where Z g (f) is the frequency-dependent complex resistance of the voice coil. It is determined mainly by three quantities: the active resistance of the voice coil R g (measured with an ohmmeter), the inductance L g. The current is also affected by the back EMF that occurs when the voice coil moves in a magnetic field and is proportional to the speed of movement.

At frequencies much higher than the main resonance, the back-emf value can be neglected, since the cone with the voice coil simply does not have time to accelerate in half the period of the signal frequency. Therefore, the dependence of Z g (f) above the frequency of the main resonance is determined mainly by the quantities R g and L g

So, neither the resistance R g nor the inductance L g differ in particular constancy. The voice coil resistance strongly depends on temperature (TCS of copper is about +0.35% / o C), and the temperature of the voice coil of small-sized medium-frequency GGs during normal operation changes by 30 ... 50 o C and, moreover, very quickly - in tens of milliseconds and less. Accordingly, the resistance of the voice coil, and hence the current through it, and the sound pressure at a constant applied voltage change by 10 ... 15%, creating intermodulation distortion of the corresponding value thermal signal compression).

Inductance changes are even more complex. Amplitude and phase current through the voice coil at frequencies noticeably higher than the resonant one is largely determined by the value of the inductance. And it very much depends on the position of the voice coil in the gap: with a normal displacement amplitude for frequencies that are only slightly higher than the fundamental resonance frequency, the inductance changes by 15 ... 40% for various GGs. Accordingly, at the rated power supplied to the loudspeaker, intermodulation distortion can reach 10 ... 25%.

The above is illustrated by a photograph of sound pressure oscillograms taken on one of the best domestic mid-frequency GG - 5GDSH-5-4. The block diagram of the measuring setup is shown in the figure.

As a source of a two-tone signal, a pair of generators and two amplifiers were used, between the outputs of which the GG under test was connected, installed on an acoustic screen with an area of ​​about 1 m 2 . Two separate amplifiers with a large power margin (400 W) are used to avoid the formation of intermodulation distortion during the passage of a two-tone signal through the amplification path. The sound pressure developed by the head was perceived by a ribbon electrodynamic microphone, the non-linear distortion of which is less than -66 dB at a sound pressure level of 130 dB. The sound pressure of such a loudspeaker in this experiment was approximately 96 dB, so that the distortion of the microphone under these conditions could be neglected.

As can be seen on the oscillograms on the screen of the upper oscilloscope (upper - without filtering, lower - after HPF filtering), the modulation of a signal with a frequency of 4 kHz under the influence of another with a frequency of 300 Hz (with a head power of 2.5 W) exceeds 20%. This corresponds to an intermodulation distortion of about 15%. It seems that there is no need to remind that the threshold of perceptibility of intermodulation distortion products is much lower than one percent, reaching hundredths of a percent in some cases. It is clear that the distortions of the UMZCH, if only they are of a “soft” nature, and do not exceed a few hundredths of a percent, are simply indistinguishable against the background of distortions in the loudspeaker caused by its operation from a voltage source. Intermodulation distortion products destroy the transparency and detail of the sound - it turns out to be a "porridge" in which individual instruments and voices are heard only occasionally. This type of sound is probably well known to readers (a good test for distortion can be a phonogram of a children's choir).

Connoisseurs may argue that there are many ways to reduce voice coil impedance variability: filling the gap with magnetic cooling fluid, installing copper caps on the cores of the magnetic system, and carefully selecting the core profile and coil winding density, and much more. However, all these methods, firstly, do not solve the problem in principle, and secondly, lead to the complication and increase in the cost of the production of HG, as a result of which they are not fully used even in studio loudspeakers. That is why most mid-frequency and low-frequency GGs have neither copper caps nor magnetic fluid (in such GGs, when operating at full power, the liquid is often ejected from the gap).

Therefore, powering the GG from a high-impedance signal source (in the limit - from a current source) is a useful and expedient way to reduce their intermodulation distortion, especially when building multiband active acoustic systems. In this case, damping of the main resonance has to be performed purely acoustically, since the intrinsic acoustic quality factor of mid-frequency GGs, as a rule, significantly exceeds unity, reaching 4...8.

It is curious that it is precisely this mode of “current” power supply of the GG that takes place in lamp UMZCH with a pentode or tetrode output with a shallow (less than 10 dB) FOS, especially if there is a local FOS for current in the form of resistance in the cathode circuit.

In the process of establishing such an amplifier, its distortions without a general OOS usually turn out to be within 2.5% and are confidently noticeable by ear when included in the break of the control path (comparison method with the "straight wire"). However, after connecting an amplifier to a loudspeaker, it is found that as the depth of feedback increases, the sound first improves, and then there is a loss of detail and transparency. This is especially noticeable in a multi-band amplifier, the output stages of which drive directly to the corresponding loudspeaker heads without any filters.

The reason for this, at first glance, a paradoxical phenomenon is that with an increase in the OOS depth in voltage, the output impedance of the amplifier decreases sharply. The negative consequences of powering the GG from the UMZCH with a low output impedance are discussed above. In a triode amplifier, the output impedance, as a rule, is much less than in a pentode or tetrode, and the linearity before the introduction of feedback is higher, so the introduction of feedback on voltage improves the performance of a single amplifier, but at the same time worsens the performance of the loudspeaker head. As a result, as a result of introducing an output voltage feedback into a triode amplifier, the sound can actually become worse, despite the improvement in the characteristics of the amplifier itself! This empirically established fact serves as inexhaustible food for speculation on the topic of harm from the use of feedback in audio power amplifiers, as well as arguments about the special, tube-like transparency and naturalness of sound. However, from the above facts, it clearly follows that the point is not in the presence (or absence) of the OOS itself, but in the resulting output impedance of the amplifier. That's where the "dog is buried"!

It is worth saying a few words about the use of negative output resistance UMZCH. Yes, positive current feedback (POF) helps to dampen the GG at the fundamental resonance frequency and reduce the power dissipated in the voice coil. However, one has to pay for the simplicity and efficiency of damping by increasing the influence of the GG inductance on its characteristics, even in comparison with the operation mode from a voltage source. This is because the time constant L g /R g is replaced by a larger one equal to L g /. Accordingly, the frequency decreases, starting from which the inductive reactance begins to dominate in the sum of the impedances of the "GG + UMZCH" system. Similarly, the influence of thermal changes in the active resistance of the voice coil increases: the sum of the changing resistance of the voice coil and the constant negative output resistance of the amplifier changes more in percentage terms.

Of course, if R out. PA in absolute value does not exceed 1/3 ... 1/5 of the active resistance of the voice coil winding, the loss from the introduction of the POS is small. Therefore, a weak current POS for a small additional damping or for fine tuning of the quality factor in the low-frequency band can be used. In addition, the current POS and the current source mode in the UMZCH are not compatible with each other, as a result of which the current supply of the GG in the low-frequency band, unfortunately, is not always applicable.

With intermodulation distortion, we apparently figured it out. Now it remains to consider the second question - the magnitude and duration of the overtones that arise in the diffuser of the GG when reproducing signals of an impulse nature. This question is much more complicated and "thinner".

There are theoretically two possibilities to eliminate these overtones. The first is to shift all resonant frequencies beyond the operating frequency range, into the region of far ultrasound (50...100 kHz). This method is used in the development of low-power high-frequency GG and some measuring microphones. In relation to the GG, this is the method of a "hard" diffuser.

So, a third option is also possible - the use of a GG with a relatively "hard" diffuser and the introduction of its acoustic damping. In this case, it is possible to combine the advantages of both approaches to some extent. This is how studio control loudspeakers (large monitors) are most often built. Naturally, when the damped HG is powered from a voltage source, the frequency response is significantly distorted due to a sharp drop in the total quality factor of the main resonance. The current source in this case also turns out to be preferable, since it helps to equalize the frequency response simultaneously with the exclusion of the effect of thermal compression.

Summarizing the above, we can draw the following practical conclusions:

1. The loudspeaker head operating mode from a current source (as opposed to a voltage source) provides a significant reduction in intermodulation distortion introduced by the head itself.

2. The most appropriate design option for a loudspeaker with low intermodulation distortion is an active multi-band, with a crossover filter and separate amplifiers for each band. However, this conclusion is true regardless of the GG diet.

4. In order to obtain a high output impedance of the amplifier and maintain a small amount of its distortion, OOS should be used not in terms of voltage, but in terms of current.

Of course, the author understands that the proposed method of reducing distortion is not a panacea. In addition, in the case of using a ready-made multiband loudspeaker, the current supply of its individual GGs without alteration is impossible. An attempt to connect a multi-band loudspeaker as a whole to an amplifier with an increased output impedance will lead not so much to a decrease in distortion, but to a sharp distortion of the frequency response and, accordingly, a failure of the tonal balance. Nonetheless reduction of intermodulation distortion GG almost an order of magnitude, and by such an accessible method, clearly deserves worthy attention.

S.AGEEV, Moscow

Usually, the issue of resistance matching is not given enough attention. The purpose of this section is to outline the principles and practice of impedance matching.

Input impedance. Any electrical device that requires a signal to operate has an input impedance. Just like any other resistance (particularly resistance in DC circuits), the input resistance of a device is a measure of the current flowing through the input circuit when a certain voltage is applied to the input.

For example, the input impedance of a 12 volt light bulb consuming 0.5 amps is 12/0.5 = 24 ohms. A lamp is a simple example of resistance, since we know that it contains nothing but a filament. From this point of view, the input impedance of a circuit such as a bipolar transistor amplifier may appear to be something more complex. At first glance, the presence of capacitors, resistors and semiconductor p-n junctions in the circuit makes determining the input resistance difficult. However, any input circuit, no matter how complex, can be represented as a simple impedance, as shown in Figure 2.18. If VIN is the voltage of the AC input signal, and IIN is the AC current flowing through the input circuit, then the input impedance is ZIN = UIN/ IIN[Ω].

For most circuits, the input impedance has a resistive (ohmic) character over a wide frequency range, within which the phase shift between the input voltage and input current is negligible. In this case, the input circuit looks like the one shown in Fig. 2.19, Ohm's law holds and there is no need for complex number algebra and vector diagrams applied to circuits with reactive elements.

Fig.2.18. A diagram with a pair of input terminals illustrating the concept of input impedance ZIN

It is important to note, however, that the ohmic nature of the input impedance does not necessarily mean that it can be measured at DC; There may be reactive components in the input signal path (such as a coupling capacitor) that are not relevant to the AC signal at mid frequencies, but do not allow measurements to be made at the DC input target. Based on the foregoing, in further consideration we will assume that the impedance is purely ohmic in nature and Z=R.

Input resistance measurement. The input voltage is easy to measure with an oscilloscope or AC voltmeter. However, AC current cannot be measured as easily, particularly when the input impedance is high. The most suitable way to measure input resistance is shown in Figure 2.19.

Fig.2.19. Input resistance measurement

A resistor with a known resistance R is connected between the generator and the input of the circuit under study. Then, using an oscilloscope or an AC voltmeter with a high-resistance input, voltages U1 and U2 are measured on both sides of the resistor R. If IIN is an alternating input current, then, according to Ohm's law, a voltage equal to U1 - U2 = RIBX drops across the resistor. Hence I BX = (U1 - U2)/R, R BX = U2 / R. Therefore If the circuit under study is an amplifier, then it is often most convenient to determine U1 and U2 by measuring at the output of the amplifier: U1 is measured with the generator directly connected to the input, and U2 is measured with the resistor R connected in series with the input of the resistor R. Since only the ratio U1 / U2, the gain plays no role. It is assumed that during these measurements, the voltage at the output of the generator remains unchanged. Here's a very simple example: if a 10 kΩ resistor in series with the input causes the amplifier output voltage to decrease by half, then U1/U2 = 2 and RIN = 10 kΩ.

output impedance. An example that gives an idea of ​​the output resistance is this: the headlights of a car dim slightly when the starter is running. The high current drawn by the starter causes a voltage drop inside the battery, causing the voltage at its terminals to decrease and the headlights to become less bright. This voltage drop occurs across the output impedance of the battery, perhaps better known as internal or source resistance.

Let's extend this view to include all output circuits, including DC and AC circuits, which always have a certain output impedance connected to a voltage source. The applicability of such a simple description even to the most complex circuits is convinced by the rule that says that any circuit with resistances and sources that has two output terminals can be replaced by one resistance and one source connected in series. Here, the word "source" should be understood as an ideal component that generates voltage and continues to maintain this voltage unchanged even when current is consumed from it. The description of the output circuit is shown in fig. 2.20 where ROUT is the output impedance, and U is the no-load output voltage, that is, the voltage at the open circuit output.

Fig.2.20. Output Circuit Equivalent Circuit

When discussing the issue of input and output resistance, it is appropriate to pay attention to the concept that appears for the first time: the equivalent circuit. All schemes in Fig. 2.18, 2.19 and 2.20 are equivalent circuits. They do not necessarily reflect the actual components and connections in the devices in question; these diagrams are a convenient representation that is useful for understanding how a given device behaves.

Rice. 2.20 shows that in the case when a resistor or input terminals of another device is connected to the output terminals, part of the source voltage U drops on the internal resistance of the source.

Output resistance measurement. A simple method for measuring output resistance follows from the circuit in Figure 2.20. If the output terminals are short-circuited, the current short-circuit current ISC is changed and it is taken into account that it coincides with the current flowing through the resistance ROUT as a result of applying voltage U to it, then we get: ROUT = U/IKC. The voltage U supplied to the circuit by the source is measured at the output terminals in the "idle" mode, that is, with a negligible output current. Thus, the output impedance can easily be obtained as the ratio of the open circuit voltage to the short circuit current.

Having considered this principle method for determining the output resistance, it must be said that there are obstacles along the way, inherent in measuring the output short circuit current in most cases. Usually, in the event of a short circuit, the operating conditions of the circuit are violated and reliable results cannot be obtained; in some cases, certain components may fail, unable to withstand an abnormally large load. A simple illustration of the inapplicability of the short circuit method: try measuring the output impedance of the AC mains! Despite these shortcomings from a practical point of view, the use of this method is justified in the theoretical derivation of the output impedance of the circuit, and it is used further in this chapter.

A practical way to measure output resistance is shown in Figure 2.21. Here, the no-load output voltage is measured with a voltmeter or oscilloscope with a high-impedance input, and then the output terminals are shunted with a load of known resistance R. The reduced output voltage with the load connected is directly determined by the same meter. The value of ROUT can be calculated as the ratio of the amount by which the voltage has dropped to the output current.

Fig.2.21. Measuring Output Resistance Using a Shunt Resistor

If U is the open-circuit output voltage and U1 is the output voltage at load R, then the voltage drop across ROUT when the load is present is U-U1, the output current when the load is present is U1/R, so ROUT= R(U - U1) / U1 Resistance matching for optimum voltage transfer. Most electronic circuits consider signals to be voltages. In most cases, when connecting one part of the circuit to another, it is necessary to transfer the voltage to the maximum extent with a minimum of losses. This is the requirement for maximum voltage transfer, which is usually met when matching resistances. Considering this criterion, we consider the principle of resistance matching.

Figure 2.22 shows two blocks connected to each other: for optimal voltage transfer, UIN should be as close to U as possible. The voltage UIN is: UIN = URIN / ROUT + RIN and UIN≈U, RIN >> ROUT

Fig.2.22. Illustration of impedance matching between two devices

In other words, for the best possible voltage transfer from one circuit to another, the output impedance of the first circuit must be much less than the input impedance of the second circuit; generally you want RIN > 10ROUT. It is for this reason that testing devices such as generators are designed with low output impedance (typically< 100 Ом). С другой стороны, осциллограф, предназначенный для наблюдения напряжений в испытываемой схеме, делается с большим входным сопротивлением (типичное значение >1 MΩ).

Fig.2.23. The dependence of the output voltage of the circuit on the load resistance

If the conditions for optimal matching of resistances are not met and the signal is fed to the input of the circuit with an input resistance comparable to the output resistance of the source, then in the most general case, there will simply be voltage losses. This situation occurs when two bipolar transistor amplifier stages, like the one shown in Fig. 11.5 are connected one after the other (cascaded). Both the input and output impedance of such a bipolar transistor stage are of the same order of magnitude (usually several thousand ohms), which means that about 50% of the signal voltage is lost in the connection between the stages. On the other hand, the FET amplifier (Fig. 11.13) is much better in terms of impedance matching: it has a very large input impedance and an average output impedance; when connecting such cascades one after another, signal losses are negligible.

There are one or two cases where impedance matching needs special attention, since too little load resistance affects not only the voltage gain but also the frequency response. This happens when the output impedance of the source is not purely resistive, but instead is reactance, and so the frequency response changes. A simple example is a condenser microphone, where the output impedance is expressed in picofarads rather than ohms, with a typical value in the region of 50 pF. Good low frequency reproduction requires the input impedance of the amplifier to be large compared to the capacitance reactance of 50 pF at frequencies up to 20 Hz. In practice, this requires an input impedance of about 200 MΩ, which is usually provided by a FET amplifier mounted in the microphone body.

Resistance matching for optimal power transfer. Although maximum voltage transfer is usually the criterion for impedance matching, there are times when you want to transfer maximum power. Without giving mathematical calculations, we will inform you that for circuit 2.22, the maximum power in RIN is achieved when RIN = ROUT. This result is known as the maximum power theorem: maximum power is transferred from the source to the load when the load impedance is equal to the output impedance of the source. This theorem is valid not only for resistive components, but also for complex components ZIN and ZOUT. In this case, it is required that, in addition to the condition RIN = ROUT, the condition XIN = -XOUT is also fulfilled, that is, if one impedance is capacitive, the other impedance must be inductive.

Resistance matching for optimum current transfer. Sometimes resistance matching is required to provide maximum current in the input circuit. Referring again to fig. 2.22, it can be seen that the maximum input current IВХ is achieved when the impedance in the circuit is chosen as small as possible. Therefore, with a fixed ROUT, one should strive for the smallest possible value of RIN. This rather unusual situation is exactly the opposite of the usual case when it is necessary to transmit voltage.