RC Circuit Limitations and Tradeoffs
Frequency and time programmability is a key feature of the RC-circuit, and it’s up to the engineer to find the right resistor and capacitor combination. A wide range of capacitor sizes and types are available, although they present tradeoffs between, accuracy, size, and cost. The best tolerance is 1-2%, using NP0/COG type capacitors. But since NP0/COG capacitors are limited to under a microfarad before they get quite expensive, the designer is likely to compromise with 5% tolerance or much worse, which is typical of other capacitor types. For very small capacitance, the designer should be aware of the error resulting from stray or gate capacitances. For example, only a few picofarad of capacitance on the comparator inputs in Figure 2 will result in a 1% error. In addition to these issues, there are other potential sources of capacitor error such as ESR, temperature coefficient, and leakage current.
With all of these capacitor issues, it may seem like a good idea to integrate the RC capacitor within the semiconductor. Since accurate semiconductor-based capacitors require significant die real estate and trimming, this is a costly solution, even to incorporate very small capacitance. Because of the limitation on the RC range and the higher cost, this is not a common option among RC-circuit devices, and the external capacitor “headache” will probably never go away.
With the practical limitations of capacitors, resistor selection becomes more critical, but they too have limitations. Very small resistance in the RC-circuit will have power consumption consequences, since a significant amount of power is wasted in the resistor(s). For example, the RC-circuit in Figure 2 draws more than a milliamp of peak current and, in astable mode (oscillator), the two external resistors by themselves draw an average current of 450 micro-amps . On the other end of the scale, surface leakage and input bias currents would place a limit on the maximum resistance. With a few nanoamperes of stray or bias current, more than 10MΩ will have an appreciable error due to these currents.
Figure 3: RC-circuit error due to comparator threshold variations.
Assuming that suitable resistors and capacitors are available, there is another significant source of error in the RC-circuit, due to the nonlinear response of the charge and discharge curve. Any comparator threshold error is amplified by a factor of >2.5 in the timing response. For example, comparator threshold errors of ±2% results in approximately ±5.4% of timing error. For astable operation, this problem not only shows up as frequency error, but also creates duty cycle error. Figure 3 illustrates this source of error. Note that the inherent error in the exponential response curve is eliminated with silicon oscillators where a linear response curve is used.
One of the advantages of programmability is the ability to implement voltage controlled modulation (VCO), pulse width modulation (PWM), pulse duration modulation and other types of dynamic time or frequency control. A long list of applications requires this capability, including tone generation, heater control, motor control, and pulse generation. The need is evident by the enormous number of web pages, books, articles, and notes dedicated to these applications implemented with 555-type or other RC-circuit based devices. Whether it’s a 555 timer or other device, the implementation with an RC-circuit requires adjusting the comparator threshold voltage or the RC response curve. Adjusting comparator thresholds is fraught with errors, as shown above. The simplest implementation of control requires the use of potentiometers or variable capacitors to adjust the RC-time. Practically speaking, most implementations require significant additional circuitry, such as a closed loop feedback network, to compensate for the many sources of error.
In summary, as each generation of electronics has continued to place more demands on accuracy, power and size, the inherent limitations of the RC-circuit have become apparent. RC-circuits don’t generally operate above 1MHz, they are inaccurate, consume significant power, and can be more expensive than first appears, especially when extraordinary efforts are made to increase functionality or performance.
The traditional alternative approach for timing circuits requires a fixed frequency crystal oscillator. Adding programmability or asynchronous functionality requires circuitry. Whether this is done with discrete components, or by programming a microcontroller, simple timing applications end up as complicated and inflexible projects. For many applications, this is just not an attractive option. With silicon oscillators, the RC-based timer has true competition.