For filter design, one can choose the resistor and capacitor value according to one's wish. But is there any disadvantage of using a high-value resistor with a low-value capacitor or vice versa?
is there any disadvantage of using a high-value resistor with a low-value capacitor or vice versa?
High impedance brings to mind:
High-value resistors create high-impedance nodes. That wouldn't be a huge problem in itself: after all, vacuum-tube circuits are chock full of nodes with load resistances in the 100kΩ-2MΩ range. But then: how familiar are you with all the design and assembly concerns that vacuum tube circuits have routinely dealt with already 50+ years ago?
High-impedance nodes are susceptible to coupling by leakage and stray capacitance to other nodes they'd otherwise not couple to. One such node of concern is the low-frequency mains wiring and fields emanating from mains transformers.
High-impedance nodes are susceptible to parasitic capacitances of the very resistors that create them. Those resistors are no longer ideal parts in such circumstances. For surface-mount parts, this matters only for frequencies well above 1MHz, though. The frequencies of concern go up as you go smaller, e.g. 0402 resistors are quite close to ideal from parasitic standpoint up to about 1GHz. Conversely, small values of 0402 capacitors (up to a couple hundred pF) are pretty ideal as well in that frequency range.
High value capacitors:
High-value capacitors generally cost more compared to lower value of the same type. The cost is often highly nonlinear and depends on production yield, market demand, etc.
High-value capacitors have high drive requirements. They are fine as long as they are connected only to high impedance nodes, but this has to be kept in mind.
As a rule of thumb, most op-amps are fine driving equivalent load reactances above 1kΩ. This would be the capacitive/inductive reactance in parallel to pure resistance. The load resistance/reactance used to specify distortion and settling time in op-amp datasheets is usually is in the 600Ω-2kΩ range. So, when going below that specification limit, you can refer to plots of distortion and output voltage range vs. load resistance if they are given in the datasheet. Outside of that you have to qualify the part for your application.
High-value capacitive loads rob op-amps of phase margin. In applications where high DC precision or high AC gain accuracy is required, you may be unable to afford isolating series resistors, and may have ringing in low-gain stages as the equivalent load capacitance goes beyond 100pF.
Now, this may not be a concern in low bandwidth applications. But even in those, you may need a high-GBW amplifier to keep the distortion down to a minimum if distortion is a concern. The highest performing audio op-amps have GBWs well in excess of 100MHz: about 3 orders of magnitude larger than the audio signal bandwidth. Such parts can't handle much capacitive loading unless they are designed for line driving applications.
High-value capacitors are typically larger, and thus have larger parasitic series inductance compared to lower values. Their larger sizes couples them more to adjacent nodes in the circuit. This is less of a concern with surface mount parts.
High-value capacitors of equivalent performance to smaller values are often much more expensive. That's why you may end up being forced to use high-value resistors to keep the capacitors small anyway. For example: in filter circuits that work from 0Hz to audio band, if you're using surface mount ceramic capacitors then C0G/NP0 types are the only acceptable ones, unless you are OK with the microphonics (your users might not be OK). Thus you can't generally use X5R/X7R nor other high-K ceramics like Z5. To keep costs down with C0G/NP0 you are limited to values well below 1μF.
Aside: audio doesn't need to be literal, only a frequency range. Most "DC" instrumentation circuits, such as signal conditioners for strain, pressure and optical measurements are quite sensitive to "audio" microphonics, and X5R/X7R/Z capacitors in the signal paths in those applications are bad news if you want high precision. They are bad news for reference voltage decoupling for A/D and D/A converters as well, unless in RF or wideband digital transmission, where audio is out-of-band. You may end up having to use tantalums in parallel with C0G types then.
High-value capacitors may force a dielectric type that's inherently more noisy, or with progressively more dielectric absorption. Vacuum and dry air and similar mixtures of single-element gases are close to ideal in terms of performance, but their volumetric efficiency leaves something to be desired. A couple hundred pF is all you can readily buy, although you can make much better parts yourself if you have the time and capability. Then comes Teflon, then various plastic films, then low-K ceramics, then high-K ceramics get mixed in with tantalum and electrolytics. If you carefully select electrolytic capacitors, you can get pretty low noise parts, but the variation between various types can be dramatic - several orders of magnitude difference in noise amplitude at low frequencies (1μHz to 1Hz, give-or-take - important if you're looking for long-term stable DC voltage references, for example).
Noise is obviously a concern in filter circuits at all frequencies. Dielectric absorption's relatively long time constant is of concern mainly at DC and in audio and similar low-frequency applications. It becomes largely irrelevant for RF use.
I've mentioned microphonics already as well - they are not quite noise (which is random/self-uncorrelated and usually wideband unless shaped otherwise by design), but certainly an interfering signal - usually quite narrowband.
Having said all that, also remember that laboratory instruments and high-performance audio gear is not everyone's market. Your application may simply not care much for low distortion, low microphonics, etc. A lot of quite acceptable consumer goods have mediocre or just average performance in terms of signal chain fidelity, and the users are not unhappy with that. Reverse-engineering junked car audio gear is a one good way to learn about low-cost low-microphonic audio signal chains.
Personally, my view is slightly skewed since I've been doing instrumentation/audio/lab gear since I was a kid. My first design for an external user was a simple portable audio mixer, where I learned about the noise of MOS op-amps and high-value resistors. I still remember: it was based on CA3240, since that's what I had available. Those parts are anything but quiet for low-ish impedance audio work.
What you're talking about is choosing the impedance of the filter.
If you were operating the filter between a zero source impedance and an infinite load impedance, then you would be completely free to implement your RC time constant with any value resistor, and the corresponding capacitor, that you wanted.
Usually however, that's not the case, and we need to operate between finite impedances. Then we would choose a resistor that's well above the source impedance, and below the load impedance.
You select filter components not
"according to ... wish" but to meet the transfer function specifications.
For opamp based circuits: anything in the 1k\$\Omega\$ to 10k\$\Omega\$ range for resistors is considered good. A comprehensive post is available for your perusal. For larger resistors, offset currents become progressively relevant.
You can search for "precision resistors" that get more expensive with demanding specs. For PCB applications, surface mount resistors are small in size. (search 0802/0603 and smaller etc)
Electrolytic capacitors consume board space; besides larger capacitors are used for lower frequency ranges, so it makes sense to achieve \$R C\$ specs using resistors where possible. The lifetime of a product is determined by the most leaky capacitor.
For precision capacitors, read up on film capacitors that get progressively expensive with tolerance specs.
To implement a resistor on chip requires expensive silicon die space. Hence depending on use, a MOS transistor with an appropriate W/L ratio is used with proper biasing. This simple arrangement suffers from process variability (meaning: the absolute value of a component can vary over quite a range). The same variability argument applies to a capacitor on-chip as well.
The good news is that ratio of resistors (or capacitors) can be made very accurate on a chip.
The main idea behind the SC concept is that a resistor is simulated by moving charges in and out of capacitor using non-overlapping clocks (whose frequency is controlled by a PLL using an external crystal and hence is very accurate). Couple that with accurate ratio between capacitors on chip, the idea becomes viable.
For high frequency applications, filtering is done using either well-characterized discrete components, of more advantageously using a PLL. That is the case for wireless transceiver circuits. A good series of articles can be found here.
Another choice for RF applications is the SAW/BAW filters.
In many cases, there is another restriction which will cause additional selection limits. Keyword: Component spread.
All second-order filter stages require a minimum of 2 resistors and 2 capacitors for establishing the desired filter function.
Depending on specific filter specifications (gain, pole-Q) the corresponding "component spread" (difference between the lowest and largest componenet values) can be pretty large. Very often, these considerations are inportant for selecting a suitable filter topolgy.
Example: Bandpass in MFB-topology (MFB: multi-feedback) with two equal capacitors and a bandwidth according to Q=10. In this case, the ratio of the two resistors must have a value of 4Q²=400.
(Hint: Additional resistive positive feedback - Antoniou`s modification - will improve the situation and decrease this component spread)
Comment: The same situation does exist for the well-known unity-gain S&K filter stage. Depending on the capacitor ratio, the required resistor ratio will be between app. 4Q² and 9Q². (Hint: In this case, change from unity gain to a gain-of-two will drastically reduce the large component spread.)
Capacitors with "high value" are usually electrolytic and the price increases and physical size increases significantly as the value gets high. A resistor is a resistor when you are talking about small signal filtering. A small SMD resistor is the same size whether 1k to 10M.
With Electrolytic resistors also comes current leakage and fairly wide tolerance bands on capacitance. The aluminized film on high value electrolytes is rolled and with those rolls comes inductance. So, you may get an unplanned inductive resonance with large value caps using rolled films.
Low value Film resistors or ceramic caps can be quite accurate and small with very low inductance - match that with a larger resistor and you'll be fine. In general, I try to stay below 1uF when I can but, that is a general phrase. Sometimes it is not quite possible. Larger value ceramic caps (tens to hundred uF) can get expensive and sometimes you have to suck it up and dish out the dollars or sometimes you have to use an electrolytic.