1. Field of the Invention
The present invention relates generally to modern control systems and, more particularly, to negative feedback loops in such systems.
2. Description of the Art
FIG. 1 illustrates a known control system utilizing a negative feedback loop in a low drop-out (LDO) amplifier application 100. This particular application 100 is configured as an LDO regulator circuit. An LDO regulator is a circuit that provides a well-specified and stable DC voltage. The lowest value of differential (input/output) voltage at which the control loop stops regulating is called the dropout voltage. Modern applications such as communication electronics and other battery-powered portable devices require a low dropout voltage and low quiescent currents for increased power efficiency. LDO regulators meet both of these design needs.
At the input stage, a reference input signal VREF is fed into the inverting input of a dual stage amplifier 104. The output from the amplifier controls a field effect transistor (FET) Q1 that acts as a switch for supplying current from the power source VDD to the load (modeled as a resistor RL in the figure). Some of the current flowing between the source and the drain of Q1 is then fed back through a simple RC filter network into the non-inverting input of the amplifier 104. This feedback signal is called VFB. The RC filter network comprises capacitor C1 and resistors R1 and R2. C1 AC-couples the output back into amplifier 104. Resistors R1 and R2 are configured in a voltage divider with R2 connected to ground. The ratio between the values of R1 and R2 may be adjusted to set the output voltage, VOUT, to a desired value.
VOUT is fed back through the RC filtering network yielding signal VFB at the non-inverting input of the amplifier. Typically, differential amplifiers are used in modern electronic circuits. Differential amplifiers amplify the voltage difference between two input signals. When the output of a differential amplifier is connected to its inverting input and a reference voltage signal is applied to the non-inverting input, the output voltage of the op-amp closely follows that reference voltage. As the amplifier output increases, that output voltage is fed back to the inverting input, thereby acting to decrease the voltage differential between the inputs. When the input differential is reduced, the amplifier output and the system gain are also reduced. In FIG. 1, because amplifier 104 is a dual-stage amplifier, the reference signal is shown connected to the inverting input rather than the non-inverting input. Nevertheless, because the output is fed back in a manner that reduces the system gain, the result is negative feedback, sometimes called degenerative feedback.
Negative feedback is often employed to stabilize a control system when the system exhibits a gain from the input to the output. The output stage 120 in this LDO application is modeled by load resistor RL and an output capacitor C0 which is needed to deliver an instantaneous current to a dynamic load. C0 has a characteristic equivalent series resistance (ESR) modeled by a series resistor RESR. ESR is an effective resistance that is used to describe the resistive part of the impedance of certain electrical components such as capacitors.
An important characteristic of this type of control circuit is the ratio between the output and input signal amplitudes, known as the transfer function. The transfer function for any given system is used to model the gain of the system as a function of the input signal frequency. Such control systems are often designed to meet the specifications of a transfer function. The frequency response of the control system is completely described by its transfer function. As such, the stability of a system over a range of input signal frequencies may be predicted based upon properties of its transfer function known as poles and zeros. A pole is a root of the polynomial denominator of a transfer function; a zero is a root of the polynomial numerator.
In designing stable systems, one important consideration is the shift in phase that a signal undergoes as it passes through the system. Poles and zeros are associated with these shifts in phase. If the signal accumulates a shift in phase of 180 degrees, the shift causes the negative feedback to become positive feedback. This is problematic when the system is operating at greater than unity gain as positive feedback will drive the system to an unstable oscillatory state. In order to maintain the stability of the control system, designers often build in a phase shift buffer, called a phase margin. For example, a 50 degree phase margin ensures that the signal never undergoes a phase shift of more than about 130 degrees (i.e. it never comes within approximately 50 degrees of a 180 degree phase shift). 50 degrees is a typical value of a phase margin in an LDO design; however, a 50 degree phase margin is not a requirement for stability and smaller phase margins of 45 degrees or lower may suffice. Furthermore, although a design goal may be to maintain a particular phase margin, the actual performance of a system may be less than the nominal phase margin value. The nominal value of the phase margin is chosen to meet the specifications of a particular design and may vary significantly.
Both poles and zeros can be introduced into the transfer function describing the control loop by inserting various electronic components into the loop. For example, a dual-stage amplifier will create two poles in the transfer function. The addition of poles and zeros into the frequency response of a system must be taken into account in order to design a system with a bounded (finite) output. Unwanted or unavoidable poles and zeros can create significant challenges when trying to stabilize a control system over a range of operating frequencies.
Previously, efforts have been made to stabilize a control system by designing the system so that troublesome poles only affect the system negligibly over the operating frequency range. This approach limits the designer to specific component values and configurations. For example, an output stage may include a capacitor having an ESR which adds a zero to the transfer function at a certain frequency. In order to realize a stable system, the capacitor must be limited to values such that the added zero does not interfere with the system response over the input frequency range. For this reason, small variations in the value of the ESR in an output capacitor can have a significant destabilizing effect on the entire system. A major goal of electronic system design is to avoid limiting circuit components to a precise value or range of values, allowing for easy replacement and substitution of components.
Another previous effort to stabilize control systems involves raising the quiescent current. The quiescent current, sometimes called the leakage current, is the portion of the input current that does not contribute to the load current. In other words, it is the current that the system consumes when no load current is being supplied. By raising the quiescent current, non-dominant poles in the system can be pushed to much higher frequency levels outside the system's normal operating range. A drawback of this stabilization method is that a higher quiescent current drains the batteries that power the system. For this reason many modern applications demand a low quiescent current for increased battery lifetime.