originally published in Russian, Technika Kino i Televideniya, 1990, No 6, pp

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1 Feedback amplifier input stage design D..Danyuk, G.V.Pil'ko (Institute of Metal Physics, Academy of Sciences, krainian SSR) originally published in Russian, Technika Kino i Televideniya, 99, No 6, pp. 6-8 Negative feedback in audio amplifier improves and stabilizes many parameters, in particular decreases the nonlinear distortion. For the same time the feedback amplifiers are susceptible to the specific transient intermodulation distortion (TIM) [], which appears as a result of the overload of the amplifying stage(s), which precede the network, which determines audio amplifier bandwidth without feedback [, 3]. Characteristic feature of the presence of TIM is the anomalously rapid increase in the nonlinear (harmonic, intermodulation) distortion with the frequency of the input signal [4, 5]. The gain of feedback amplifier can be written as Ws (), β() s + Gs () β() s where β( s ) is the attenuation ratio of the feedback network ( s - complex frequency); Gs ()- amplifier gain without feedback. The greater will be loop gain Gs () β () s, the more precisely W()approaches s a desired value β( s ). For the existence of TIM the input signal of the first stage ош ()has s a great importance: ош вых вхw() s вх () s Gs () Gs () Gs () β(). () ()grows ош s with the decrease of loop gain, reaching вх at Gs () β () s. If the BJT long tail pair with the bound of the active operation of ~5 mv (-4 dbu) [6] is used in audio amplifier, which works with the input levels of...+6 dbu, then TIM will be inevitable. This is correct for the input signal without rolloff at high frequencies. et us examine expression () in detail. Assume an amplifier with single pole frequency response and the bandwidth without feedback ω. With frequency-independent overall feedback it follows from (): () s s + ω ω ( + β( s) G( s)) ош вх вх s + ω, () s + ω where ω - amplifier bandwidth with feedback. The diagram of equation () is given in Fig. (curve ). In Fig. the bound of the active operation of input stage is depicted (straight line ). When the input voltage of the first stage (curve ) exceeds the line () (to the right of point A) TIM is generated. If the bound of the active operation of the input stage will be extended more than ош (), s then will be no intersection point (the input stage will be within active region) and TIM will not appear. This can be achieved by application of local current

2 feedback or by replacement of the active element (by field-effect transistors (FETs)). The emitter resistors value for BJT long-tailed pair (Fig. ) can be calculated by the formula [7]: Fig.. Frequency dependences of the input signal of the first stage of feedback amplifier (), bound of the active operation of the first stage without local feedback () and with local frequencydependent feedback (3) R I вх (3) where I - quiescent current of long tail pair. The same expressions can be obtained for FET long tail pair and single transistor stages. The local feedback decreases the long tail pair transconductance IR ϕ Т times and, consequently, the gain G() s also ( I 4ϕ Т - long tail pair transconductance with R, ϕ Т 6mV at C). The elements of frequency compensation network, which determine the bandwidth ω, should be proportionally changed so that ω would remain unchanged. If one considers that the real audio signal has the natural rolloff at frequencies higher ω с or the input low pass filter with the cutoff frequency ωс < ω is used, then condition (3) can be rewritten in the following form: R вх с ω I ω (4). As it is noted in [8], during the calculation according to formula (4) the statistical dependence of spectral energy distribution in the musical programs [9] should be considered. That is equivalent to selection ω с of several khz. The local feedback has negative consequences: it considerably decreases the loop gain of the overall feedback at low and medium frequencies. The nonlinear distortion, which originated in the power stage, thus gives larger contribution in overall distortion. Emitter resistors increase the thermal noise of amplifier. It is substantial for the BJT input stages, which operated with the low-impedance signal source.

3 Fig.. Diagram of the long tail pair stage with frequency-independent (without the inductor ) and with frequency-dependent (with the inductor ) local feedback It is possible to remove negative consequences of local feedback by it decrease at low and medium frequencies. This can be achieved by adding an inductor in the local feedback network (see Fig. ). In that case the long tail pair transconductance g m and the bound of the long tail pair active operation гр becomes the functions of frequency (see Fig., curve 3): g m gm R Rg + R ( R g + ), (5) m m where g m - transconductance of the long tail pair without local feedback ( g BJT long tail pair); г I R ( Rgm + ) р ϕ T ( Rg m + ), (6) g R m I ϕ - for m 4 where гр ϕ Т - the bound of active operation for the long tail pair without local feedback. It follows from expression (5) that the inductor leads to the additional phase shift at the frequency ω Т ω ϕ( ω ) arctg R arctg ( R g m + ) ω.(7) R From the condition of the absence of oscillation phase shift at the frequency ω should be not exceed 8 ; it is also undesirable that it would exceed 5 as a result of the huge

4 resonance peak at the frequency ω (+6 db) and the long ringing at the output with the step input. sing expression () or (3), it is possible to obtain the resistor values of the local feedback network, and then, taking into account the measured or calculated phase shift and required phase margin at frequency ω, get the value from (7) R Rg tg ( ( )) ω π ϕ ω. (8) m It is easy to apply expressions (5-8) to FET long tail pair and single transistor stages, substituting there the appropriate g m value. If the amplifier bandwidth without feedback ω is determined by the output resistance of the first stage and by the input capacitance of the second one, then with frequencydependent local feedback the additional loop gain will be obtained R () s R ( R g + ) m relative to the amplifier with frequency-independent local feedback in the input stage and s + ω R ( s) ω ( R g + ) R ( R g + ) m m relative to the amplifier without local feedback. Additional loop gain leads to the appropriate decrease of nonlinear distortion. The correctness of the obtained expressions was checked in the evaluation audio amplifier, examined into [5]. At the output level + dbu on the load 6 Ohm the application of frequency-dependent local feedback with the loop gain of 6 db in the input long tail pair make it possible to increase the slew rate of output signal from,7 to 3 V/us with the constant level of harmonic distortion at the low frequencies. The disconnection of inductor leads to the increase of the harmonic distortion 6-4 times at the frequency below khz. Conclusions Application of the local frequency-dependent negative feedback in the stages of the audio amplifier, which precede the network, which determines the bandwidth of amplifier without feedback, makes it possible to decrease the nonlinearity and to remove transient intermodulation distortion The correctness of proposed simple method of application the frequency-dependent local feedback in the amplifier input stage of the audio amplifier is confirmed experimentally. References

5 .Ososkova I. N. Transient intermodulation distortion and the reason for it appearance in audio channels during the record of musical programs (in Russian). Tehnika kino I televideniya, 98, No, pp Cherry E. M. Transient intermodulation distortion. Part - Hard nonlinearity. - IEEE Trans. Acoustic, Speech and Signal Proc., 98, ASSP-9,, p Cherry E. M., Dabke K.F. Transient intermodulation distortion. Part - Soft nonlinearity. - JAES, 986, 34, /, p Tihonova.S. The analysis of the sensitivity of the standard methods of measuring the nonlinearity to the dynamic distortion Tehnika kino I televideniya, 985, No 7, pp Tihonova.S. The analysis of the frequency dependences of the criteria of the nonlinearity of audio-frequency amplifiers with external feedback - Deposited manuscript NIKFI (All-nion Scientific Research Institute Of Motion Pitures And Photography) No 5KT -D V. I. Anisimov, M. V. Kapitonov, N. N. Prokopenko, Yu. M. Sokolov. Operational amplifiers with the direct coupling of stages - eningrad: Energy, 979, pp each W.M. An amplifier input stage design criterion for the suppression of dynamic distortion. - JAES, 98, 9, 4, p Garde P., Amplifier first-stage criteria for avoiding slew-rate liming. - JAES, 986, 34, 5, р Methods of measurements for radio transmitters. Part : Bandwidth, out-of-band power and power of non-essential oscillations. Publication IEC Geneva, 978. Afterword When we wrote this paper we were not aware of Deane E. Jensen Operational amplifier circuit S Patent 4,87,479, Sept.98 and it realization in JT99C discrete op amp. A careful investigation will reveal different circuit and different design approach.

ELC224 Final Review (12/10/2009) Name:

ELC224 Final Review (12/10/2009) Name: Select the correct answer to the problems 1 through 20. 1. A common-emitter amplifier that uses direct coupling is an example of a dc amplifier. 2. The frequency