Hello,
I am trying to learn electronics and since last Wednesday I am trying to understand simple low pass, high pass etc filters based on capacitor+resistor circuit. I studied some theory behind this, and, in general, I have two pictures in my head:
But when I see some schematics, usually for devices that measure biological signal I see something slightly different which I do not understand. According to images above, high passfilter is made out of a capacitor and resistor connected in a serial, in a way that second leg of a resistor goes to the ground, and its first leg connects with capacitor and goes to Vout. But in some schematics I see that these components are connected in a line, like Vin-C-R-Vout, or even parallel (depending on filter type) but still described as low pass/high pass filters.
A capacitor has an impedance that varies with frequency, so any circuit using them will have
a response that depends on frequency. Unfortunately there are many many filter circuits possible,
both passive and active, so a full explanation is a course on linear systems and filter theory...
In both those circuit snippets there's an opamp in inverting configuration, which acts to multiply a
signal by the ratio of two impedances, something like
Vout = - Vin x (Z_R1 + Z_C1) / (Z_R2 || Z_C2) { where Z_C1 is the impedance of C1, etc }
And to actually make such equations work you have to move to complex numbers - without that
its hard to start explaining the circuit response (well ordinary differential equations would suffice).
The real issue is that impedances do not add like resistances do, impedances are more general and
complex values.
I am trying to understand simple low pass, high pass etc filters based on capacitor+resistor circuit
Stick to your topic "understand simple low pass, high pass". Don't worry now about the opamps and anything else except "simple low pass, high pass filters". Do you understand "simple low pass, high pass filters" yet ? If not, what is your question about them?
aaandrew:
But in some schematics I see that these components are connected in a line, like Vin-C-R-Vout
In that case, the resistance (and thus filter frequency) is determined partly by the load itself. Sometimes you don't exactly know what that load's R value will be... so you have to generalize. Audio is a good example. It's common to have an op-amp driving an analog line-out to RCA or 3.5mm jacks through a 100R resistor and, say, a 1uF capacitor. What's the filter knee here? Depends on on the input impedance of the device you connect to! If it were just the 100R resistor, it would be a 1.6kHz high-pass! Luckily, in consumer audio land, we can assume the input of the next device is going to be at least 10K, which forms a 16Hz high-pass (or subsonic filter, or DC blocking filter -- whatever name you'd like to give it.) This is why slightly higher input impedances (say, 22k) are good. Then the filter knee is at 7Hz, which is hardly interfering with audio content anymore. Although, you need to be careful about how many times you split a signal with Y-cables, as the load impedances become parallel to each other and drop accordingly. (This is why splitting a line-out too many ways causes distortion from too much output current draw, and poor frequency response from the changing filter points.)
aaandrew:
or even parallel (depending on filter type) but still described as low pass/high pass filters.
Parallel R and C do something different. When you have a cap in series, it becomes high impedance as frequency drops, until it's effectively infinite at DC. If you place a resistor in parallel, you've created an alternate route for current to take that is NOT frequency-dependent. Then, instead of DC impedance being infinite, it's determined by the resistor -- since the resistor is lower impedance than infinity, it will be the route taken by current at low frequencies. At and above the knee point of the filter (which is determined by the cap and the input impedance of whatever the next part of the circuit is), the balance starts to shift and the cap becomes the lower impedance path instead of the resistor. So low frequencies are never completely cut off, they're just impeded by the resistor. High frequencies go through the cap with lower impedance, up to (theoretically) 0R at infinite frequency. (Of course, in real life, the cap will have inductance that rolls off frequencies above some point also.) Between DC and infinite, the cap's impedance and resistor's resistance are in parallel.
100R = 100 ohm. IIRC, the "R" indeed stands for resistance, although you'll see the notation on other parts as well. Probably just from ubiquity, and at this point, convention. Typically used in the place of a decimal point (4R7 = 4.7) since printed component values tend to be small on discrete parts and a "." would be hardly visible, and possibly hardly printable. Used in typed communications because not many people have an Ohms key on their keyboard... but just about everyone has an R.
The case is more complicated than I thought but the reason is that I only read about passive low/high pass filters. Now everything is more clear, but there is still a lot to learn.
I also found a book about "Design and development of medical electronic instrumentation" which maybe useful for more advanced users interested in this topic. Type the title in google and follow the first link for a pdf.
C8 is (simplistically) a high pass filter. However, it is in the negative feedback loop of an Op Amp, so you get -more- negative feedback as frequency goes higher, which makes the Op Amp act as a low pass filter. As you observed, C7 is acting as a high pass filter, again as part of the feedback loop but in this case it increases gain with frequency and makes the Op Amp act as a high pass filter.
It is a bit more complex than you characterized it, but the general idea is that with the high pass action formed by C7 lower than the low pass action of C8, the entire circuit has more gain at frequencies between those two inflection points.
The capacitive reactance, resistance, negative feedback, and gain of the Op Amp result in much better performance and different characteristics than a simple RC filter. You can get better than -20dB/decade, more or less passband ripple, different phase performance, etc.
