series capacitors and high pass filters - Page 1
Forum section: electronics / beginners

author: electrolust
author_rank: Unknown
timestamp: October 05, 2015, 08:40:02 pm
content: Next in my lineup of capacitor questions!! Now I am finally getting to some practical application as well.I guess that the total capacitance of capacitors in series is the reciprocal of the sum of reciprocals. The tutorials all say we can replace a number of series capacitors with a single one -- of course this is a drastic simplification that doesn't take ESR and all the other stuff into account.My question is how does this affect the corner frequency of the high pass filter a capacitor would form in series with a load?I have a portable 2-way radio that supplies electret mic power over the mic+ signal line. I have a unpowered dynamic mic as these perform "best" for my application. I am blocking the DC bias to the mic with a 10uF electrolytic cap (film caps are physically too large). In testing it works great.I chose 10uF by guessing at a 2k2 impedance on the radio's mic input -- 10uF with 2k2 impedance is a 7.2Hz corner frequency. I chose that based on an article stating that this range is a good corner frequency for high fidelity audio. Note my application is only telephone quality voice though. The PSTN passes 300Hz to 3400Hz. The low end of that frequency band is above the human voice fundamental frequency but the brain fills in the missing fundamental frequency from the harmonics. My point though is that the 7.2Hz does not have to be so low (if my guess on 2k2 is correct), I just chose this because, why not.The radio has its own coupling cap, since the bias voltage is supplied on the mic+ line and has to be removed for the radio's amp input.After I chose the 10uF and built my own circuit, I found a radio schematic. The radio's cap is a bipolar .033uF. From there it passes into an ASIC processor, so I don't know what the rest of the mic input circuit looks like. If we stick with the assumed 2k2 impedance, the results in a 2200Hz corner frequency (not considering my part of the circuit). This seems far too high to me.Isn't 2k2 a reasonable mic input impedance to expect? Such a small onboard capacitor suggests a much larger mic input impedance, does it not? At 10x the impedance (22k) we'd have a 10x lower corner frequency of 220Hz, which seems reasonable enough for 2-way radio voice even if it misses the fundamental, like PSTN does, but I still get the feeling this is low.When I consider my own 10uF capacitance, this creates a combined series capacitance of 0.0329uF. Basically no change! And of course there is no change, considering my capacitor is several orders of magnitude larger than the radio's. Certainly the combined series capacitance is well within the tolerance range of a typical single capacitor. And so it makes sense that my circuit works, regardless of what the ultimate corner frequency is.But I just want to verify if the series capacitance has the same effect in a high pass filter as it would it there were a single capacitor. I'm not convinced that it does.This will be important to my choice of capacitor value on my side of the circuit. The smaller I can go, the more likely it is that I can use a film cap. Which I understand is better for this application. If I can disregard the value of my own capacitor w.r.t. corner frequency, I don't have to try to figure out the radio mic impedance or select for it.

author: electrolust
author_rank: Unknown
timestamp: October 06, 2015, 05:12:26 am
content: Ah-ha! I ran a circuit simulation. I will state the name of the site just so as to help validate the result. circuitlab.When I create a circuit with 10uF capacitance in series with a 2.2k load, I get my expected -3dB corner frequency of 7.2(ish) Hz.When I create a circuit with 5uF capacitance in series with a 2.2k load, I get the expected -3dB corner frequency of 14.4(ish) Hz.When I create a circuit of two 10uF series capacitors in series with a 2.2k load, I get a -3dB corner frequency of 14.4(ish) Hz. So at least according to the circuitlab simulator, the series capacitors do act as a single capacitor (of 5uF in this case) with respect to the high pass filter formed with the resistive load.I guess I need to figure out why that is. But in practical terms I guess I need to measure the impedance of the mic input to help me determine a cap value that makes sense.

author: Psi
author_rank: Super Contributor
timestamp: October 06, 2015, 05:25:29 am
content: Electrically you shouldn't be able to tell the difference between multiple passive components in series or parallel and a single one.Obviously the uF value will change and the esr as well but it will still act like a single cap with those specs.Of course, if you tap off the series terminations with anything all bets are off

author: electrolust
author_rank: Unknown
timestamp: October 06, 2015, 05:35:48 am
content: Ah, this plot helps me understand it. I added a probe at the midpoint between the 2 capacitors.Instead of thinking about it as 2 caps in series followed by the resistor, if I think about it as a cap followed by (capacitor and resistor in series), it's very obvious what should happen.