So I am doing a small project of optimization of components tolerance to reduce the impact of circuit sensitivity to meet a project specification.
Right now I am with 5% resistors and inductors and 3% capacitors.
My question is if there is a common design rule or not that we should try to reduce sensititvy of resistors or capacitors in terms of costs? Does anyone know if there is any information published about that?
Thank you
Generally it is much cheaper to get tight tolerance resistors than capacitors. You might find that even 5% resistors are mostly within 1% since the manufacturing process for resistors has become very good.
Capacitors on the other hand are much harder to make with very tight tolerance, so you generally pay more.
So if you have a choice, I would pick tight tolerance resistors and looser tolerance capacitors.
2% and 5% COG capacitors are used mainly in RF matching circuits where the designer wants to match/adapt the input impedance of an antenna to the output impedance of the RF amplifier.
COG capacitors are stable in value over a wide range of temperature.
In 25 years of circuits design I've seen tight tolerance capacitors in RF circuits only.
Ceramic, Electrolytic, Film, Tantalum, and Polyester capacitors are commonly manufactured, sold, and used with a 10 to 20% tolerance.
Yet, if the performance of a circuit is based on the tight tolerance of one of these capacitors, then it's not a reliable design because the value of the capacitance may exceed the tolerance over the time.
The real challenge in the capacitors world is not the quest for the tightest tolerance capacitor. It's reducing its size at a given capacitance value.
Murata for example is now able to produce a ceramic capacitor of 10 µF in a 0402 package. Ten years ago that was just a dream.
Tight tolerance (such as 0.1%) resistors are not expensive these days. At the 1% level they're barely more expensive when all is considered than 5% unless your quantities are immense. Maybe less expensive if you only have to stock 1% (perhaps except for a couple values for pullups and LEDs). High stability with temperature and time similarly is not so expensive.
On the other hand, precision capacitors are not cheap and generally unavailable at a sensible price at better than 1% tolerance. If you can use NP0 ceramic of relatively low value they are not too bad in stability and price, provided you don't demand tight tolerance.
Inductors tend to be at least as bad as capacitors. Better than 1% tolerance is pretty much unavailable as an off-the-shelf product.
So you'll likely get the most bang for your buck by choosing tight tolerance resistors and moderate tolerance capacitors or inductors where the overall performance is determined more-or-less by the product of the two.
Also, trimpots are generally less expensive and more available than trimcaps, and adjustable inductors are not very common at all.
Of course the ideal situation is to design your circuit so it is less sensitive to the values, perhaps by self-tuning or by doing the filtering digitally.
I suggest going to the website of a distributor who carries a wide range of such parts in appropriate values for your situation and simply comparing price and availability of various combinations. Ideally you want to see multiple suppliers at an affordable price and plenty in stock right now.
It's impossible to answer really without knowing your application area. You'd probably need to describe your circuit/application in more detail. I'd say that your question is way too general as it stands.
Assuming that the circuit can be designed to accommodate large tolerances without significant rise in complexity, having large margins in the circuit will reduce cost. If mixed domain is available, then calibration can be done on the digital side of things. That's usually the cheapest, and then the circuit should be designed to allow 10-20% capacitor tolerance; often even more will be possible. 1% resistors are cheap, so there's little advantage in choosing 2% or 5% unless you're making 10k+ quantities, and even then you must contrast the savings with the cost of engineering time involved.
If there's an MCU "in the loop", then you can cut production line costs by self-calibrating using an internal transfer standard. If the costs allow the MCU to run from a sufficiently accurate oscillator - e.g. an internal precision oscillator (IPO) or an external quartz - then you already have a good time standard. You're also likely to have reasonably good voltage reference built into something - another standard to use. Then, if you need precision resistor ratios - you can have perhaps just one precision ratio that can be affordable at a precision better than 1% of the ratio. Most MCUs have ADCs that have total error much lower than 1%. Then you'd design the rest circuit so that those cheap standards can be used to calibrate the rest of the circuit.
It is often possible to convert approaches that require absolute time standard into those that only require ratio-relative time measurements, and in that case almost anything reasonable will be stable enough, especially that your relative error requirement seems to be in the 0.3-1.0% ballpark.
If the MCU is out of the loop but has enough supervisory capability, you can use digital potentiometers or other techniques to trim the analog circuit in situ, without production line involvement. For example, you can use DAC or PWM waveforms to produce offset voltages. You can also use PWM that controls a series switch to synthesize variable circuit elements: as long as the switch is commutated much faster than the bandwidth of useful signal in the circuit, the switch's duty ratio will act as a 0-100% scaler for the attached series resistance or capacitance, or if connected in parallel it will scale an inductance. This works well into the audio frequencies, and allows e.g. variable continuous-time filters that are controlled directly by GPIO or perhaps buffered GPIO. With clever enough design, you may be able to tightly intertwine the GPIO drivers on the MCU with the analog circuit's nodes.
