Negative feedback

The negative feedback, also called negative feedback, is a central element of a control loop: A part of the output variable UA is fed back to the input so that it counteracts the input signal UE. In many systems, there are those control mechanisms that restrict growth in a natural manner and stabilize. In technology, the principle is used in many ways.

While the negative feedback amplifiers by reducing distortions in the foreground, it goes in the regulation longer step response and transient response.

Voltage feedback of an operational amplifier

Operational amplifier ( OP) are designed so that the specifications of the overall circuit can be defined almost entirely by the external circuit of the OP. For this reason, their properties can be very simple and easy to describe.

General stability

Wherein each operational amplifier, the gain with increasing frequency and the output signal is reduced with a certain delay following the changes in the input voltage. Because the exact dates affect the interpretation of the negative feedback significantly, they are specified in each data sheet:

• In the transit frequency fT the gain to the value 1 (or 0 dB) has decreased (red dot in the picture). In still higher frequencies, the feedback can not bring the operating criterion in accordance with the stability of Barkhausen to oscillate.
• With sinusoidal input voltage, the output voltage is out of phase. The phase shift is represented by the angle β (blue bar above). If β for all f < fT remains in the range 0 < β < -180 ° and the external feedback circuit adds no additional phase shift, the OP can not oscillate.

The difference between 180 ° - | β | is called the phase margin or phase margin φ ( engl: phase margin ), as a measure of how easily the amplifier is working. The closer this value is 180 °, the more stable working the negative feedback. The larger β is, the smaller is φ, and the circuit reacts after jumps of the signal amplitude always " nervous " at the amplifier output can be observed stronger overshoot. If φ is negative, has become a positive feedback from the negative feedback and the amplifier acts as an oscillator. In control theory, it is recommended that the phase margin should be at about 50 °.

The value of β can be influenced by internal or external frequency compensation of the operational amplifier.

Reducing the gain

The adjacent circuit of the voltage divider generates the share

The output voltage Ua. Where 0 < α ≤ 1, the feedback component is subtracted from the signal in the operating voltage Ue and the difference appears to the factor V amplified at the output as Vout. Solving the corresponding equation, it follows

The approximation is usually sufficiently precise, when the gain exceeds 105. Then, the overall gain of the circuit is Ua / Ue practically determined only by the negative feedback. It may be surprising that the gain is intentionally reduced. This one is buying enormous advantages: the bandwidth is increased, the manufacturing tolerances of the OP have no meaning and the characteristic of the OP is linearized ( less distortion ).

Independence of parameters

The properties of electronic components are temperature dependent, the construction is spread and by aging. For example, if the open-loop gain V of the OPs halved, the total gain varies only insignificantly. The gain of the operational amplifier itself is usually non-linear and would actually rise to signal distortion. However, since operational amplifiers are always used strong negative feedback, they are among the most linear circuits. It is sufficient if the gain in the vicinity of the zero point (the difference voltage of the two inputs) significantly greater than the total gain of the application. Only through the systematic use of negative feedback are the properties of analog amplifiers reproducible.

Reduction of the output resistance

If the output of an amplifier load, the output voltage decreases. The circuit behaves as if the cause would be a non- bridgeable internal resistance Ra immediately before the output. A voltage negative feedback information, so to speak the amplifier input via the voltage drop, which then provides much more tension that the target voltage is again almost produced. Overall, the effective internal resistance is reduced to

Example: An operational amplifier has the open-loop gain V = 105 and R = 20 Ω. When a voltage divider with α = 0.01 is chosen, the effective output resistance is only Reff = 0.02 Ω. This reduction is highly desirable in most applications.

If an increase of the output resistance is necessary, this can be achieved by a current feedback (see the constant current source).

Increasing the bandwidth

In a negative feedback amplifier, the gain bandwidth - product is constant and is called transition frequency fT. A change in the negative feedback effect on the gain, and thus the bandwidth.

• When the gain of OP fT = 1.3 MHz is set by ( low ) negative feedback to V = 100, it has a bandwidth of 13 kHz.
• Decreases at higher feedback gain to 10, the bandwidth is increased to 130 kHz.
• At stärkstmöglicher feedback ( α = 1), the impedance converter, the range extends to Ft.

Reducing distortions

In any amplifier ( without feedback ) the output voltage is exactly proportional to the input voltage, a connection which is depicted in the form of a curved characteristic. The greater the curvature, the greater harmonic content and distortion factor k of the output voltage. Both of which can be reduced by negative feedback. Since an OP the " open-loop gain" ( without feedback ) is always greater than 10000, a strong negative feedback will be chosen and it applies to the total harmonic distortion:

When a transistor or a tube with substantially reduced ground reinforcement is used in place of only about 50 of the OP, the distortion due to feedback can not be lowered arbitrarily. Another special feature is observed when, instead of the OP, a component is used with quadratic characteristic, such as a field effect transistor:

• Without negative feedback dominates the quadratic distortion ( 4%), while the cubic distortion is barely measurable (0.04 %).
• At low negative feedback, the quadratic distortion decreases, for example, 2%, whereas the cubic distortion initially rises to 0.1%.
• With increasing negative feedback fall both ways. Since the quadratic proportion always outweighs the distortion can not be reduced below about 1% due to the low basic gain even at very strong negative feedback. For this reason, it is usually better to combine several levels by a strong " over- all negative feedback ", as each amplifier stage gegenzukoppeln separately.

Limits the negative feedback

Counter- Coupled amplifier show at continuous signals with small amplitude changes usually benign behavior. The timing, however, can contain surprises when a pulse (single, fast rise- operation, part of a square wave ) reaches the input of a negative feedback amplifier. The reason for this lies in the very wide-band spectrum of a square wave, the little fainter extends up to extremely high frequencies. However, an OP no longer amplified beyond its transit frequency fT and it takes a short period of time until the amplified signal appears at the output. This has nothing to do with overdrive and the resulting even more serious consequences.

During this time, the negative feedback has no effect ( the loop is "open"), then a " rounder " function of lower slew rate of the input signal is subtracted, which is exacerbated by a capacitive load at the output.

The high-frequency spectral frequencies beyond fT can not in principle be compensated by negative feedback. This leads to the transient signal variations (so-called " overshoot " and Gibbs phenomenon ), which are all the greater, the nearer the amplifier to its instability limit ( phase boundary ) works.

The phase behavior is also influenced by the load, which is why audio amplifiers are particularly affected because the operated on them loads ( speaker ) have a strongly frequency-dependent impedance curve.

Methods have also been developed to avoid or compensate for certain disadvantages of the negative feedback by means of additional circuits.

Negative feedback amplifiers with problematic

Problems always occur when the phase shift is not so smooth curve shows how the top image. This is true for all RC - coupled amplifier, which have an upper and lower frequency limit. Here, even at weak feedback a " phase margin" be achieved from almost zero, which is sometimes desirable to increase low frequency ( "bass booster "). Problems at the upper frequency limit, there is always the use of output transformers in tube amps that provide in the vicinity of resonances for strong phase shifts. If the transformer generates a phase shift of 180 ° at 20 kHz ( phase margin φ = 0 °) is determined from the feedback oscillating positive feedback and the circuit. There are only two antidotes:

• The gain is lowered sufficiently far ahead of 20 kHz, as required by the stability criterion of Barkhausen. This height reduction is usually undesirable.
• The negative feedback will be adjusted so weak that it is almost ineffective.

Applications

• If in a fish pond, the population of predators, so reduces the amount of food available individually, slowing further growth, stops or even reverses. (Example: Wator )
• A heating system is reduced when a certain temperature, the supply of additional energy. In this way, the further temperature rise slowed down.
• Electronic components such as transistor amplifiers, operational amplifiers, or the electron tube, a linearization of the transfer characteristic curve is obtained by the negative feedback, this leads to a reduction of the distortion ( THD ) and a linearization of the frequency response. At the same time, the output signal is not so much determined by the reinforcing properties of the active device. It should be noted that at high frequencies because of the unavoidable phase shift of the negative feedback, a positive feedback is. This can lead to unwanted oscillations if the total gain is not sufficiently reduced due to the frequency compensation.
• In biology, the principle of negative feedback is among other things the pupillary reflex to high light or closing the stomata during drought. Especially in endocrinology, the end products of a hormonal axis have an inhibitory effect on the formation of upstream hormones back: for example, blocks the thyroid hormone triiodothyronine both the formation of thyrotropin-releasing hormone ( TRH) from the hypothalamus and that of the thyroid -stimulating hormone thyrotropin in the pituitary gland (hypophysis ). Particularly important are feedback in the development of biological rhythms.