Frequency compensation
Sub frequency compensation is defined as the internal or external wiring of an electrical amplifier , such as an operational amplifier , on the one hand, a stable operation without oscillations ensure and on the other hand, overshoot to reduce when this with negative feedback is operated.
motivation
Both amplifiers and operational amplifiers are internally composed of several amplifier stages, which in turn are made up of transistors and resistors. However, signals do not pass through transistors at random speed; rather, the (amplified) output voltage follows the input voltage with a short delay of a few nanoseconds. OPs also have internal capacities that have to be charged and discharged first and can delay the phase by up to 90 °. Both effects together cause a phase shift that becomes more and more serious with increasing signal frequency and number of stages and can significantly exceed the 180 ° mark at high frequencies (in the adjacent picture at 7 MHz) and many amplifier stages.
In the practical use of an amplifier, use is made of negative feedback, also known as negative feedback . For example, a voltage divider made of resistors leads from the output back to the inverting input.
At high frequencies, but the intended effect is reversed: The recycled output voltage is due to internal phase shift of the OP too late to, from the negative feedback is a positive feedback (positive feedback) and the circuit now has an important characteristic of an oscillator .
Oscillation condition
An amplifier can be turned into an oscillator through feedback . Around 1930 Harry Nyquist found the conditions under which a permanent oscillation in the output signal occurs. These are known as the Nyquist criterion :
- The loop gain must be at least 1 at this frequency (no attenuation).
- The phase shift of the feedback loop must be a multiple of 360 ° at this frequency.
Nothing can be changed about the increasing phase shift with increasing signal frequency, unless the number of internal amplifier stages is reduced to one. But you can't build an amplifier with it. So you have to reduce the loop gain to less than 1 before the phase shift reaches the critical value.
Since a negative feedback corresponds in principle to a phase shift of 180 °, since it feeds the inverted signal back to the input, the oscillation condition is already fulfilled when a further 180 ° of phase shift is added within the negative feedback loop.
compensation
The usual measure is a small capacitor of a few picofarads between the collector and base of a transistor in an emitter circuit , which, because of the Miller effect, reduces the gain with increasing frequency. This leads to a dominant pole in the transfer function of the amplifier, which dominates the phase shift of the amplifier over a wide frequency range and holds it at 90 °. This guarantees stability as long as there is no further 90 ° phase shift in the negative feedback before the loop gain drops below 1.
The loop gain becomes greater, the stronger the negative feedback of the amplifier, i.e. H. the lower the gain of the overall circuit is set. For this reason, negative feedback amplifiers with a low overall gain, e.g. B. voltage followers, more unstable than those with a large overall gain. The negative feedback thus also influences the minimum size of the capacitance required for frequency compensation. Since an unnecessarily large capacity limits the bandwidth of the amplifier, it can make sense to leave the choice of a suitable capacity value to the user, who can adapt it exactly to the situation in his circuit. In practice, this leads to the following alternatives:
- The capacitor is built into the operating theater and dimensioned for a total gain of 1. The OP is then referred to as fully compensated , because it is also stable as a voltage follower without further measures (example: OP27). Such an operation is particularly easy to use, which is why the majority of operations offered are fully compensated.
- The capacitor is built into the operating theater, but is only dimensioned for an overall gain of over 1 (e.g. 3, 5 or 10). Such an OP is partially compensated , has a higher gain bandwidth product, but cannot be used for smaller overall gains without further measures (example: OP37, otherwise identical to the OP27). Such OPs are chosen when the higher overall gain is present in the circuit and one wants to benefit from the higher bandwidth.
- The capacitor has to be supplemented externally, an internal capacitor is missing. The housing is provided with additional connections for this purpose (example: LM301A). This externally compensated variant is the most flexible because the user can determine the optimal values himself.
The dominant pole is the reason why the gain-bandwidth product of the VV-OPV is constant and can be listed as an amplifier property in the data sheet. In the case of externally compensated OPs, this value depends on the externally connected capacitor and can therefore only be given as a diagram.
A ring oscillator is basically a negative feedback 3- or 5-stage amplifier without frequency compensation so that it works as an oscillator. The cut-off frequency of the individual stages can be calculated from the generated frequency if the possible transit times are not dominant compared to the phase rotations.
literature
- Ulrich Tietze, Christoph Schenk: Semiconductor circuit technology . 12th edition. Springer, Berlin 2002, ISBN 3-540-42849-6 .
Individual evidence
- ↑ Data sheet of the OP27 from Analog Devices (PDF; 433 kB).
- ↑ Data sheet of the OP37 from Analog Devices (PDF; 575 kB).
- ↑ Data sheet of the OP27 / 37 from Texas Instruments
- ↑ Data sheet of the OP27 / 37 from Linear Technology
- ↑ Data sheet of the OP27 / 37 from Maxim ( Memento of the original from September 28, 2009 in the Internet Archive ) Info: The archive link was inserted automatically and has not yet been checked. Please check the original and archive link according to the instructions and then remove this notice. (PDF; 3.5 MB).
- ↑ Data sheet of the LM301A from Texas Instruments (PDF; 1 MB).
