Slew Rate Control

Slew rate of operational amplifiers is defined as the maximum rate of change of the output signal in response to changes in the large input signal. Ideally, the amplifier output under large signal conditions should follow the input signal. However, limitations on the slew rate cause the amplifier output response to be slower than the rate of change of the large input signal. The greater the slew rate the more closely the output signal follows the input signal. Various techniques have been developed to increase the slew rate of operational amplifiers. Examples of such techniques are described in U.S. Pat. No. 3,668,538 issued June 6, 1972, to Hearn and U.S. Pat. No. 3,688,208 issued Aug. 29, 1972, to Kandiah.

The present invention provides a new and useful technique for increasing the slew rate of an operational amplifier. To increase slew rate without impairing amplifier stability, additional capacitance is added to the amplifier circuit. This capacitance may be connected in parallel across the current source. The value of this capacitance is calculated according to the equation.

FIG. 1 represents a schematic diagram of a conventional operational amplifier of the differential type to which has been added the additional capacitance according to the invention, which figure should be consulted for an understanding of the mathematical derivation of the invention set out in the description of the preferred embodiment of the invention.

FIG. 2 is a graphical representation of the amplifier transconductance.

Referring to FIG. 1, the amount of current available to charge the compensating capacitor C.sub.H is limited in a conventional operational amplifier to a constant value, proportional to current I.sub.o in current source. In turn, the current I.sub.o produced by the constant current source defines the transconductance of a differential input and thus the bandwidth of the amplifier. To increase the slew rate, the I.sub.o current has to be increased. If this current is increased, then the amplifier compensating capacitor C.sub.H must be increased to insure amplifier stability. However, an increase in the compensating capacitance value limits amplifier slew rate. To increase the amplifier slew rate without impairing amplifiers stability, an additional capacitance calculated according to the equation ##EQU3## is provided.

To understand my invention, one should consider first the small-signal behavior of a feedback operational amplifier whose gain function contains a single pole. The gain-bandwidth product of such system is constant and is equal to the small signal bandwidth, i.e.: ##EQU4## where k=Boltzman constant;

T absolute temperature (.degree.Kelvin); and

q=charge.

The small signal bandwidth determines the highest frequency, which an amplifier will pass without attenuation. The relation between frequency response and time response is expressed in the definition of rise time: ##EQU5## where W.sub.-3dB is the -3dB radial frequency, or the pole of an amplifier.

The rise time is the fastest rate of output response under small-signal input excitation. Knowing that the GBW product (for open loop gain A.sub.OL) is: ##EQU6## for a given A.sub.OL, I.sub.o, C.sub.H, the bandwidth w.sub.-3dB will be limited to a finite value. Thus the fastest rate of the output signal is limited also. It is noted that the small signal input excitation is restricted to a voltage range where an amplifier still operates in the linear mode. As can be seen from FIG. 2, under large signal conditions, the transconductance of an amplifier is no longer a linear function of input signal, .vertline.E.sub.in .vertline.>E.sub.1

The maximum available current Ic.sub.H determines the highest rate of voltage change .vertline..DELTA.E.sub.o .vertline. at the compensating capacitance C.sub.H. It is called slew rate: ##EQU7## Stability considerations do not allow an increase of the slew rate, SR, by increasing I.sub.o and/or decreasing the compensating capacitance C.sub.H.

According to the teachings of the present invention, the operational amplifier is provided with additional transient current by connecting capacitance, C.sub.c, across the amplifier current source, I.sub.o. The value of C.sub.c is determined in such a way that the slew rate of an amplifier equals or exceeds the slew rate of the output signal under small signal conditions, thereby increasing the amplifier slew rate under large signal conditions above the maximum slew rate determined by the amplifier small signal characteristics.

Returning to the amplifier illustrated in FIG. 1, transistors Q.sub.1 -Q.sub.5 represent the basic operational components of a conventional differential type operational amplifier. The compensating capacitance C.sub.H is selected to determine the basic amplifier bandwidth. In accordance with the teachings of the present invention, the capacitance C.sub.c is connected across the current source I.sub.o. The invention is best described with reference to a mathematical derivation as follows:

Let:

.DELTA.I.sub.1 =the incremental current flow in the collector-emitter path of transistor Q.sub.1.

.DELTA.I.sub.2 =the incremental current flow in the collector-emitter path of transistor Q.sub.2.

.DELTA.E.sub.in =the incremental portion of the input voltage.

.DELTA.E.sub.o =the incremental portion of the amplifier output voltage. ##EQU8##

The incremental collector-emitter current through transistor Q.sub.1 can be defined by the equation: ##EQU9##

The incremental collector-emitter current through transistor Q.sub.2 can be defined by the equation: ##EQU10##

The incremental amplifier output voltage, .DELTA.E.sub.o, is given by: ##EQU11##

Substituting equations (1) and (2) for .DELTA.I.sub.1 and .DELTA.I.sub.2, respectively, in equation (3), the output voltage is given by: ##EQU12## since s=jw, the gain equation for unity gain becomes: ##EQU13##

Equation (5) represents the limiting factor for maximum slew rate, when the output signal .DELTA.E.sub.o follows input signal .DELTA.E.sub.in (both signals expressed in incremental vector form). Equation (5) may now be used to calculate the value of C.sub.c, the additional capacitance needed to increase slew rate under large signal conditions.

Equation (6) is developed directly from equation (5) by squaring both sides of the equation and setting the radial frequency w=w.sub.1 (the bandwidth under large signal conditions) to give: ##EQU14##

Equation (6) is now solved for the additional capacitance, C.sub.c as follows: ##EQU15##

For C.sub.c real the following condition has to be satisfied:

As previously described: ##EQU16## Therefore: ##EQU17## The highest radial frequency w.sub.1 will exceed the small signal BW by at least a factor of two and by a maximum up to a factor of three. So for a given h.sub.ib, C.sub.H and desired w.sub.1 the necessary C.sub.c can be calculated.

Operational amplifiers are often fabricated using integrated circuit technology. An integrated circuit operational amplifier incorporating the features of the present invention will advantageously include the compensating capacitance integrated with the integrated amplifier. Either of two manufacturing processes are conventionally used to fabricate integrated amplifiers. These are termed, respectively, the junction isolation process and the dielectric isolation process. Proper operation of the invention requires accurate implementation of the capacitance to thereby produce a capacitance of the required size. As will be recalled, the compensating capacitance, C.sub.c, is according to the teachings of this invention, connected across the current source, I.sub.o. In the case of an amplifier fabricated according to the junction isolation process, there exists a parasitic capacitance across the current source, which capacitance varies over a broad range as a function of wafer thickness and substrate bias. This variation of parasitic capacitance directly affects the value of the compensating capacitance and, therefore, capacitance external to the integrated structure would have to be utilized in order to offset the variations in parasitic capacitance value and develop a shunt capacitance across the current source which is of the required value according to the teachings of the present invention.

The dielectric isolation process may be advantageously used to produce the slew rate control circuit of this invention with the compensating capacitance fully integrated with the amplifier structure. With the dielectric isolation process, the integrated current source is produced within a semiconductor island dielectrically isolated from the device substrate. The semiconductor island capacitance, which can function as the compensating capacitance, depends only on island size and the thickness of the dielectric isolation. Thus, compensating capacitance of desired characteristics can be integrally formed with the current source by controlling, during the fabrication process, the island size and dielectric thickness. The resulting structure is a fully integrated slew rate control circuit according to the invention described hereinbefore without external components.