[islandlabs] Low Pass Filter for the $5 Transmitter

Joe toolfox at gmail.com
Thu Aug 26 20:44:05 EDT 2010


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

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; 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.

Here's a quick comparison for the curious:

http://www.dspguide.com/ch20/1.htm




Joe





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