Alex Lapayev. Analog Input/Output Compensated.

...soon everything will be digital, but the ear and tongue will remain analog...

Long ago a friend of mine showed me an article about an electronics engineer. When it was time to retire, he spent his savings on an expensive audio system, synthesizers, measuring devices and the like. Having set up synthesizing and measuring equipment in the study, he also set up everything in terms of audio signal processing in the cellar. Thus, a signal of a complicated form was synthesized, sent to the cellar, where it was modified, recorded, reproduced, restored in the form and sent up to be compared with the initial one. The equipment was perfect - both signals coincided on the oscilloscope screen - without distortions. That was nirvana...

When I finished reading, my friend told me with a sad smile: "This is what you'll have in the future". Well, it was noticed long ago that a sinusoidal wave view has a magical effect. On second thought...

Modern processing of audio and video information is almost completely exposed to digital signal processing, which gets more qualitative and cheaper from year to year. However, input and output circuits often remain analog. A clear analog audio and video signal. Everybody knows what is needed for it. Flat frequency response, small linear and harmonic distortions, and linear or uniformly decreasing phase response. Let's leave the topic on digital signal processing for other publications and talk about simple input and output buffer analog circuits.

1. Analog Input Compensated

An audio circuit input capacitor together with input impedance form a high-pass filter, which in its stop band distorts the signal form. I think it's erroneous to consider Fc selection in the range of 10-20Hz a good thing - we've got rumble filter, which prevents the audio signal from infralow frequencies, for example, for vented speaker systems protection. It's commonly known that the ear is sensitive to phase distortions only of mid-band frequency, let's say from 400Hz to 4kHz. Experiments show that in this frequency band a human can hear phase distortion already starting with 10 degrees. But what do we have in the low-band frequency? It's a well-known fact that in this case the ear is hardly sensitive to phase distortion and we can hear no difference. Usually it's true, but we can still hear the out of tune sound but normally at degrees greater than 10.

As a result opinions divided. Two ways are possible. The first one is to use high-quality capacitors of small capacity and have phase distortion using rumble filter. The second one is to have flat phase and magnitude in the infralow area by increasing the capacity up to tens microfarads, which involves irreplaceable electrolytic capacitors and this is not good. Especially when working without a DC shift. Though using audio capacitors (for example, ELNA-RFS-35V101MH5#) improves the situation. And still...

In the late nineties while developing brand new output analog audio drivers for big telecom stations I faced the following problem. I had to provide linear frequency response working with a long line through capacitors of quite small capacity since electrolytic capacitors couldn't be used due to many reasons. That's when I thought about the idea of frequency response and phase response compensation at low-pass frequency range. I think that high-quality ceramic and film capacitors of small capacity, for example, audio polypropylene should be used, which enables impedance increase compensation with frequency drop using the feedback. Thus we can get almost perfect frequency response and phase response in the low-frequency part of the operating range.

That's how the idea to compensate the dependence of audio driver impedance on frequency came to life. Here we should divide negative feedback by voltage into two parts: negative feedback with direct-current voltage (DC) and negative feedback with alternating current voltage (AC). They should be calculated so to reach frequency response cut compensation and phase response change at low frequency. If we need a rumble filter, then a compromise should be made. We will talk about it later.

1.1. Non-Inverted Schematics

The figure below shows the principle of an input non-inverted analog buffer amplifier or preamplifier with compensated frequency response and phase response. Everything is quite simple as you can see. Negative feedback by voltage is divided into negative feedback with DC voltage (R_fbdc) and negative feedback with AC voltage (R_fbac + C_fbac). To receive maximum linear frequency response in low-frequency part, time constants of input circuit and feedback circuit should be compensated:

CR Input Time Constant = CR Feed Back Time Constant

It is obvious that when changing input signal frequency, input complex impedance and total voltage gain change synchronously (increasing or decreasing) by one law, compensating frequency response cut and phase response increase in the low-frequency band. Voltage gain on DC should be greater than voltage gain on AC (R_fbdc / R_fbac ratio). This allows the circuit to compensate frequency response and phase response changing total voltage gain according to frequency by a certain law.

Due to this a small input capacitor is used, which makes it possible to use a ceramic or film capacitor instead of an electrolytic one.

If CR_Input Time Constant and CR_Feed Back Time Constant are not equal, phase and frequency responses in low-band frequency will mutually change in the opposite direction, which can be useful. The detailed examples are provided below.

Interesting fact. No matter how high voltage gain of modern operational amplifiers is, it gets down quickly with the frequency increase. As it is known, it leads to a number of frequency and phase response distortions including pulse responses. The mentioned compensation principle requires extra gain from the operational amplifier but only in the most low-band frequency part, where it causes no problems and has no influence on total qualitative scheme indices. Looking ahead, we can see in section 3. Practice some practical schemes with the compensation principle of input and output analog circuits. The scheme in Figure 45 shows output audio driver loaded on the line through a cheap analog switch of 74HC4066 type. The best representatives of the class have 30 Ohms resistance and THD level not less than 0.05% (usually they both are lower). Diode (antistatic) protection is used together with cheap electrolytic capacitors. Earlier it led to THD level higher than 0.2%, which was mostly noticeable in low-signal frequency. After compensation, THD level became not higher than 0.007% in the whole audio frequency band. The scheme is simple and has no expensive parts.

Figure 01 shows the scheme of an input non-inverted amplifier with compensated amplitude and phase responses. Gain = 3 (+9.5dB). Figure 02 shows phase and frequency responses. Main ratios are:

C (μF), R (kOhms), CR time constant (ms).

Negative feedback by voltage is divided into two parts: negative feedback with DC (R_FBDC - R4) and negative feedback with AC (RC_FBAC - R2C2). CR_Input Time Constant = CR_Feed Back Time Constant. Figure 03 shows the dependency between phase and frequency responses on the accuracy of this formula.

As you can see, input impedance is 50 kOhms and capacitor capacity is only 1μF at the scheme input, which allows for a high-quality capacitor, for example, a polypropylene instead of an electrolytic one. Phase response became more linear; phase distortion at 10Hz is just 1.2 degrees. Fc (-3dB) decreased significantly to 0.2 Hz. See Figure 02.

If using a standard scheme with the same nominal values of R1 and C1, Fc would be as follows:

Figure 04 shows one more scheme of an input non-inverted amplifier with compensated amplitude and phase responses. Gain is about 1 (Gain = 0.065dB). It should be noted that it seems impossible to get exact gain voltage equal to 1 using this scheme. Input capacitor is only of 0.1 μF capacity.

Figure 05 shows phase and frequency responses. The main ratios are the same as in Figure 01.

Interesting fact.If we add Kph coefficient to the formula for calculation of capacitor C2 nominal value basing on the graphics from Figure 03, as it is shown below, output phase response will get more flat in the low-frequency part and become almost linear in calculations. Frequency response gets a slight increase (about 1dB) in the low-frequency part, which doesn't interfere and even can be useful. See Figure 06.

1.2. Inverted Schematics

In this section we'll focus on the principle of analog signal magnitude and phase compensation in low-frequency part as applied to OpAmp inverted switching. The example is shown in Figure 07, 08, 09. I think this scheme is more preferable for using compensation principle than the scheme of inverted amplifier first of all due to its simplicity. When calculating, we need just to make the input circuit CR time constant and the feedback circuit CR time constant equal as well as tie them up to the voltage gain cascade. Main ratios are:

The input capacitor has a relatively small nominal value of - 1μF, which allows for a high-quality polypropylene capacitor instead of an electrolytic one. Input impedance is 50 kOhms. Phase and amplitude responses got linear in the lower part of the band, and low work frequency moved far to the left side of the diagram.

Figure 09 shows comparative characteristics of signal magnitude and phase before and after an input capacitor is used and right at the scheme output.

Interesting fact. Likewise in the case of non-inverted amplifier (page 9), if Kph coefficient is added to the calculation formula of C2 capacitor as it is shown below, then output phase response will get maximum flat in the low-frequency band, and become almost linear in calculations, while frequency response will get a little increase in the most low frequency band. See Figure 10, 11.

2. Analog Output Compensated Schematics

This chapter describes circuit design of output analog schemes. It's getting more complicated and challenging, as there are lots of problems with qualitative analog audio and video outputs. For example, it refers to widely used output consecutive analog switches that bring noticeable harmonic distortions. Or diode, or varistor protection, which is also far from being harmonic. Moreover, there is a specific problem with the way an output analog driver works at low-resistance load. It relates to professional audio and video systems, radio devices, audio used in high noise conditions, audio and video automotive, video drivers and transmitters, etc. As a rule, typical load impedance bogey is 75/150/300/600 Ohms. There's always a good reason to increase the capacity of output capacitors to infinite limits when operating at low-resistance load. As a minimum, you need to increase it up to tens of microfarads in order to get rid of signal phase and magnitude distortion at output. It's quite obvious that to achieve this, irreplaceable electrolytic capacitors are used again. Unfortunately, they bring their notable contribution to high noise and distortion increase in the output signal. Quite often you have to confine yourself to the capacity of 5-50 microfarads simply because of their size. Sometimes you simply cannot use electrolytic capacitors in radio devices due to line DC voltage reversal and also due to their low reliability. It's a problem to solve. Let's use the principle of magnitude and phase compensation in this case. See Figure 12.

Figure 12. Analog compensated output principle

So the schemes considered earlier had two initial time circuits each (CR time constant) - RC_INPUT and RC_FB, now we have one more connected with a C_out output capacitor. Now it's not that easy to calculate scheme parameters, because, firstly, C_out capacitor is loaded at complex circuit impedance consisting of R-load, C_FBAC and R_FBAC, and, secondly, the amplitude of input exciting voltage for an output circuit (OpAmp output) is not frequency harmonic and depends on several factors simultaneously. See Figure 13, 14.

Figure 14 based on output driver example (Gain=2) shows how output voltage OpAmp compensates C_out reactive impedance depending on the frequency. The more Gdc (Rfbdc / Rfbac) ratio is, the better it is for compensation but the worse for the scheme dynamic range. For example, with the amplification coefficient of 6dB, the output voltage peak OpAmp will reach 26dB (frequency 5-6 Hz). In other words, if the maximum level of the input signal is 0 dBu (0.776 V/rms, 1.095/amp, 2.191V/p-p), then the output will have 4.382V/p-p, and OpAmp output will have 4.382V/p-p at its maximum point! It means that the voltage level +/- 22V will be at its limit. (Not considering OpAmp real output characteristics). You should always remember this when using this schematic solution.

2.1. Main Ratios

Figure 15 shows the practical scheme of an output analog audio driver. The calculations are made according to the formulae shown above. The scheme upper channel is built on the principle of compensation, while the lower one - according to the standard scheme. For a relatively simple characteristics comparison, nominal vales of input and output capacitors and CR time constants correspond to one another on both schemes. R_input = 50 kOhms, Gain=1, Fc_6dB=5.1Hz. The capacity of input and output capacitors is comparatively small (0,51μF and 0,33μF). You can easily do without electrolytic capacitors.

Figure 16 shows the dependency between the following signal levels:

• Point after input capacitor (TP-A)
• OpAmp output point (TP-OpAmp)
• Output driver point (OUT_A)

The comparative diagrams of frequency and phase response of compensated (RED) and standard (BLUE) schematics are shown in Figure 17.

Figure 16 clearly demonstrates how OpAmp output voltage compensates reactive and resistive impedance of the output circuit (C_out + R_line). Frequency response gets notably flat in the low-frequency band and steeper in the stop band. The attenuation is 11-12dB per octave instead of 6 dB. The details are shown in Figure 17.

Interesting fact.Important! The scheme is very stable when operating at a reactive load, as the output series resistor R_line has minimum influence on the scheme output characteristics. Thus, resistance can be increased up to the desired level during the driver work at a reactive (for example, capacitive) load.

You should also note that one more asset of the schematics principle is the harmonic and linear distortions sum compensation, which is caused by the driver output circuit. As it is known, such schemes outputs often use antistatic protection (diode or varistor) or analog switches that cause quite a high level of harmonic distortions. Output capacitor, usually electrolytic one, in its turn causes a number of distortions including harmonic ones. The scheme provided allows compensating distortions almost completely and clearing the input signal from them.

However when using analog switches, which disable driver output load (R_line on the scheme), you should always remember that the feedback circuit always remains connected to the load (R_fbac and C_fbac). This may cause an unwanted, though small enough signal in the load, since the scheme becomes disbalanced in the out-of-load mode. Since R_fbac is much higher than R_load and just several times lower than R_fbdc, the level of acquired distortions is nearly missing. The best way in this case is to switch off the driver input together with the driver output, which can be done by delivering zero potential to the scheme input.

2.3. Supplement

It is fair to say that maximum linear frequency response in the low-frequency part of band has two C_out values with constant scheme parameters. It means that C_out equations have two solutions. The first value (Small Capacitor) is used mostly in practice and is shown in calculations while the second one (Large Capacitor) has a greater nominal capacity value and I think has no practical usage. That's why we'll skip calculations and theory related to this topic. Figure 18 shows the scheme of the output driver, the upper channel of which is built with C_out high nominal value - Large Capacitor while the lower one with low nominal value - Small Capacitor.

Capacitors nominal values differ greatly - 2.0μF and 1400μF. Figure 19 shows frequency and phase response diagrams with the use of Large Capacitor and Small Capacitor. It is clearly seen that scheme characteristics with the nominal value of 1400μF are shifted far in the low-frequency part of the band. Though it should be noted that in practice you can get such frequency and phase responses if the whole scheme of compensated output driver is calculated wisely using C_out small nominal value (Small Capacitor).

3. Comparison

I would like to spend some time to describing the main characteristics of 3 main types of the given schemes. Let's describe the above-mentioned types as follows:

• Compensated input. Non-inverted schematics
• Compensated input. Inverted schematics
• Compensated output schematics

Figure 20. A,B,C show examples of the given types of schemes. Figure 21 shows their frequency response and phase response. To make it look clearer, such parameters as time-setting circuits of input circuits (CR time constant), input impedance, gain and FBDS/FBAC ratio are shown equally for all examples.

It's obvious that the first two types of schemes (Compensated Input) with one RC circuit each behave as high-pass filters of the first order and have 6dB octave attenuation. While having equal initial parameters (CR time constant of input circuits, R-input, gain and FBDS/FBAC ratio) the inverted scheme has got better phase and amplitude response against the non-inverted scheme. The third type of scheme is Compensated Output, which has two RC-circuits, behaves as a high-pass filter of the second order, and has 12dB octave attenuation. FC and linear part of phase response are moved to the right along the frequency response line. For comparison: Fc Inverted Scheme=1Hz, Non-Inverted Scheme Fc=1.8Hz and Compensated Output Scheme Fc=12.3 Hz.

Having come to a conclusion of the above-mentioned comparison, it would be interesting to take a look at the behavior of the given types of schemes at more or less equal Fc cutoff frequencies. Figure 22. A,B,C show schemes with theoretical Fc cutoff frequency at about 1Hz. Figure 23 shows their amplitude and phase responses. It's clear that at comparatively equal Fc, the non-inverted scheme has twice higher CR time constant of input circuit than the inverse scheme, and compensated output scheme has a 10 times higher one. At equal input impedances, it will require the corresponding capacity increase of the input capacitor, which is not always wanted. But it needs to be specified that the type of scheme described as Compensated Output in general has a different purpose than the schemes of input compensation.

Now let's talk about dynamic features of the given schemes. Figure 24, 25 show examples of pulse (transient) responses. It's quite expected that schemes of the first order (Compensated Inputs) have better pulse responses than schemes of the second order (Compensated Inputs and Output), which have quite similar responses with Chebyshev filter of the same order. The main difference is that the main purpose of the output compensation is to get maximum linear frequency response in the operating field, and it's known that the purpose of the Chebyshev filter is the maximum steep response of cutoff frequency. See Figure 26.

Hereby we finish the massive theoretical part devoted to the method of compensating the low frequency part of frequency and phase responses of input and output analog driver schemes. Further on, we will see the most interesting part - applied real-life working schemes that use the above-mentioned principles.

3. Analog Input and Output Compensated Schematics. Practice

I think it would be fair to start describing applied devices with the presentation of the very first scheme, which uses the above-mentioned principle of compensation. As it was mentioned above, in the late nineties of the past century I faced a challenging task. We needed a brand new input-output analog driver for city telecom stations. We needed a driver that could provide an exceptionally clear reception and transmission of audio information at long distance (up to 20 km) by means of a common bidirectional line. The situation was aggravated by transmission of both audio signals and signals managing negative voltage of several volts. For correct functioning of hybrid systems and noise protection, receivers and transmitters schemes should have equal and quite evident impedance and should be in compliance with the communication line. The size of devices also meant a lot. Transformers and electrolytic capacitors couldn't be used at all. That's how we came up with the idea of using film capacitors of a small size and capacity instead, and compensating impedance change from frequency by means of negative feedback. And that's how the idea of audio driver impedance compensation was born. Here's the scheme in Figure 27.

3.1 Ultralinear Hi-Fi Preamplifier

And now we'll talk about Hi-Fi. It is known how important and often conflicting the requirements to the input cascade of a high-quality amplifier are. On the one hand, you should provide a wide frequency band and on the other hand you shouldn't let anything unwanted pass. You should find a compromise.

Figure 28 shows a practical scheme of a balanced high-end audio preamplifier built with the use of the compensation principle described above. Frequency and phase response in the operating part of the band have a smooth characteristic. See Figure 29. In infrasonic frequency range, preamplifier frequency response falls sharply thus blocking the unwanted noises of infralow frequency at the scheme input.

Input impedance is 50 kOhms, quieting sensitivity is 0dBu, voltage gain is 1.0 in the whole operating frequency band. Frequency response deviation in the 1Hz - 1kHz frequency band is not higher than 0.06dB. A small high-frequency cut is caused by only blocking capacitor C5 and can be compensated easily if needed.

Thus, the present scheme using high-quality film input capacitors of a small nominal value - 1.5μF has quite high frequency and phase response parameters. When OpAmp LME 498xx is used, THD level doesn't exceed 0,0001% (-120dB). But I think the scheme is ultralinear and has excessive capacity in the lower part of the frequency band. If it is not necessary, it is better to narrow the frequency band in the lower part. The scheme with a narrow pass band in the lower part of frequency range is shown in Figure 30.

3.3 Ultralinear Hi-Fi Preamplifier with Rumble Filtering

Interesting fact.Vented speaker system and passive radiator speaker system take a leading position on the world market of speaker systems. According to some reports, they amount to 80% of the total small and medium class speaker systems production. When using such speaker systems, you should always remember that the loudspeaker becomes completely undamped and enters piston action mode at frequencies lower than those of vent (or passive radiator). At this point, the loudspeaker will behave as if it has no baffle. But the loudspeaker isn't designed for that and it can lead to its physical destruction. On the contrary to the sealed box speaker system, where the loudspeaker winding would burn out rather than its cone gets broken.

That's why when the amplifier works with a vented or passive radiator speaker system, you should always limit the ultralow part of the audio range to protect the loudspeaker from destruction. It's better to do it quite sharply but with care in order not to limit the level of wanted low frequencies and not to distort the signal phase, which is quite contradictory. The scheme of such preamplifier is shown in Figure 32. It's a practical scheme of a balanced high-end preamplifier with rumble filtering.

As you can see in Figure 33, the scheme frequency response has a slight increase in the low frequencies band (about +1,3 dB), and then it falls and has the same rejection level as in Figure 30 of about 6dB per octave. Phase response, on the contrary, has a smooth characteristic. The method was described in detail on page 13 (Figure 10, 11). A slight increase at the end of low-frequency band doesn't spoil the sound or cause muttering but rather raises SPL at wanted frequencies, helping small and medium class speaker systems, which vent adjustment frequency is usually about 30Hz or higher.

This is perhaps my favorite scheme in its class. I make a good use of this principle in my current business projects.

3.3 Linear Audio Driver

Now it's turn of practical output analog schemes. Figure 37 shows a high-quality audio driver designed for a low-resistance load of 600 Ohms. Cascade voltage gain is 1.0, low cutoff frequency on 3dB level is 5Hz. The scheme contains only high-quality film capacitors of small capacity. Figure 38 shows frequency and phase responses of the present scheme.

3.4 Linear Video Driver

Figure 39 shows the example of a video driver scheme designed for a standard load of 75 Ohms. The gain equals to 1.0, lower peak frequency range at -3dB level equals to a half-frame sweep of 60Hz. The scheme contains only high-quality film capacitors of comparatively low capacity. Figure 40 shows frequency and phase responses of the given scheme.

3.5 Ultralinear Balanced Audio Phones Driver

Let's take a look at one more type of an audio driver working with a precise line match. It is a bidirectional analog audio scheme with an input hybrid system (not shown in the figure) loaded on a bidirectional pair line. In addition to the desire of having the maximum linear frequency and phase responses, there is one more quite important requirement - the output part of the scheme must have zero impedance in the whole range of operating frequencies. In this case, the scheme output impedance will depend only on series resistor at driver output, and the cascade will perfectly match the opposite load, and the hybrid system will perfectly split input and output signal flows. Figure 41 shows such a scheme.

R load balanced 600 Ohms.

As we can see in Figure 41, the scheme has a balanced output and is composed of direct and inverse channels loaded on the line through analog switches (Switch Ra and Rb). For example, we choose 40 Ohms impedance for open switches. The gain is 1.0. The output impedance is 300 Ohms. Figure 42, 43 show frequency and phase responses, and Figure 44 shows inverse current inflowing into driver at line input signal voltage 1V/RMS.

The given scheme has the following advantages:

• Smooth linear frequency and phase responses in the operating frequency range
• Compensation of active impedance of open audio switches on the output signal
• Compensation of reactive impedance of output capacitor on the output
• Compensation of the output signal harmonic distortions due to nonlinearity of open audio switches and output capacitor
• Output impedance close to zero in the entire operating frequency range

Interesting fact.Everyone knows that during analog audio signal transmission there is a real problem with noises of industrial power grid frequency and their harmonics. The given scheme has a good ability of common mode rejection while using hybrid system for input signal processing. This is possible thanks to consistency of driver output impedance (which is also input impedance for the input signal) in the entire operating frequency range including its lower part.

As you can see in Figure 44 the scheme has good constant output impedance in the entire operating frequency range, which equals to 8 Ohms. It makes this scheme easily adaptable to the line impedance factor and to the opposite load by standard means of switching the series resistor at output.

3.6 Linear Balanced Audio Driver With Low-Pass 44kHz Filter

Let's take a look at another interesting scheme. It's a high-class balanced audio driver designed for a 10 kOhm load. See Figure 45. For comparison, the upper channel is built according to the principle of compensation, and the lower one is built according to the principle of standard circuit design. For example, output capacitors of both channels have the same nominal values. The gain equals to 0 dB. The scheme contains a low-pass act filter of the second order with the cutoff frequency of 44 kHz. The resulting frequency and phase responses of the upper channel are shown in Figure 46 and 47, and Figure 48 shows GDT. Due to commercial reasons, passive elements nominal values are not shown on the scheme.

The driver is loaded on the line through a quite cheap 74HC4066 analog switch. The best representatives of this class have transfer impedance of not less than 30 Ohms, and the THD level is not better than 0.05% (as a rule both of them are worse). Also diode (antistatic) protection and cheap output electrolytic capacitors are used, which also doesn't make the output signal more linear. Earlier, all this resulted in the overall level of THD of more than 0.2%, which was quite notable in the low-signal range. After applying the principle of compensation, the THD level became not more than 0.007% in the whole audio frequency range. Moreover, the scheme is simple and does not have expensive parts. No doubt that it is nice to take a look at the diagram in Figure 46.

For comparison, Figure 49 shows low-frequency parts of the frequency response of high (compensated) and low (standard) channels in detail (Figure 45) at equal input and output impedance values. The difference is clear not only in the level of low operating frequency range, but also in linearity of the frequency response in its lower operating part, and in steep roll-off of its response at the cutoff frequency (6dB and 12dB).

Figure 50 shows a combined diagram of frequency and phase responses of high (compensated) and low (standard) channels (Figure 45) with equal input and output impedance values. Diagrams speak for themselves.

And here comes the conclusion. Figure 51 shows several frequency responses of the higher compensated channel with deviations of the output capacitor nominal value from its optimal (design) value. You need to pay attention to the fact that response deviation from the needed level is not so significant, given real variation of capacitors parameters, which makes the usage of the compensation principle commercially suitable, which was proved many times in practice.

Hereby let me finish. Should you have any questions or suggestions I'll be glad to hear them.