[islandlabs] Low Pass Filter for the $5 Transmitter

Jonathan Dahan jedahan at gmail.com
Fri Aug 27 13:21:26 EDT 2010

On Thu, Aug 26, 2010 at 8:44 PM, Joe <toolfox at gmail.com> wrote:

> On Thursday, August 26, 2010 01:11:37 pm Jonathan Dahan wrote:
> > On Thu, Aug 26, 2010 at 11:02 AM, Burns, William <burns at cshl.edu> wrote:
> > > Joe:
> > >
> > > I assumed that a low pass filter would have a capacitor in series with
> > > the signal.
> > > This filter is putting inductors in series instead.
> > > It's interesting, but I don't know nearly enough about LC circuits to
> > > figure out why multiple inductors are being used and what the component
> > > values should be.
> > >
> > With an inductor, the induced magnetic field resists alternating current
> at
> > a strength directly proportional to the frequency being applied, so high
> > frequencies are attenuated more, and low frequencies are allowed to pass.
> >
> > With a capacitor, a low frequency provides enough time for the capacitor
> to
> > fill with charge, essentially letting the signal pass after a short time,
> > while high frequencies will not fully charge the capacitor, and therefore
> > attenuate more.
> >
> > I am not sure if this is the correct explanation, but it makes sense in
> my
> > head. Wikipedia confirms inductor for high filter, capacitor for low
> > filter.
> Your explanation is a "variation on a theme," but its close enough.

Is it incorrect? I was trying to look at _why_ the impedance increases -
something along the lines of building up a charge on one side of the plates
over a longer time (low frequency) works, whereas a short time on either
side means no appreciable voltage.

> Remember
> what I was mentioning about impedance the other night: The impedance of a
> capacitor is inverse to the frequency.

That was the word I was looking for, impedance.

> Capacitors block DC. DC can be thought of as AC with a frequency of 0 Hz.
> Bill, if you keep the impedance/frequency relationship in mind, you'll see
> that having the capacitor shunt to ground gives a path of lesser resistance
> to
> higher frequencies. The higher the frequency, the more it wants to "jump
> down
> the rabbit hole."
> Also, the design has multiple filter nodes, (this one is a 7-pole filter)
> to
> increase the slope of the cutoff.

> >
> > Combining low and high filters gets a band pass, so if we want we can add
> > some LC circuitry to filter out frequencies under say 28Mhz, just for
> > giggles, though (can a HAM confirm this?)
> A spectrum analyzer should confirm or deny this, but I believe that the
> output
> of the oscillator can IS our fundamental frequency;

Ahh duh!

> we shouldn't have anything
> below that. Even if the internal crystal is running at 3rd or 5th overtone
> to
> get to the desired output frequency, the lower harmonics are supressed by
> the
> nature of a Pierce oscillator (that's the type of oscillator that uses a
> quartz crystal as the feedback element).
> A bandpass filter might be overkill and add unnecessary expense, but we
> should
> keep it as an option if push comes to shove.
> On the subject of filters: Look up the difference between a Chebyshev
> response
> and a Butterworth response in filter design. We're going for the former
> because
> its slope past the cutoff frequency is dramatically steeper than the flat
> Butterworth approach. Yeah, the Chebyshev has ripple in the passband, but
> we
> don't care about that because our fundemental tone is close to the cutoff.
> cool info, thanks

> Here's a quick comparison for the curious:
> http://www.dspguide.com/ch20/1.htm
> Joe
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