# Sine wave multiplication

#### geft

Joined Dec 8, 2011
19
A radio receiver is designed using a band-pass filter with frequency centered on 455kHz. It can be tuned to different stations by multiplying the incoming signal by a sine wave of correctly chosen frequency. The incoming signal is a 600kHz sine wave. What must be the frequency of the multiplying sine wave to make the signal pass through the filter?

All I have is a trigonometric identity. I'm confused. How do I even multiply sine waves?

#### MrChips

Joined Oct 2, 2009
26,811
You have two choices, 600-455 kHz or 600+455 kHz, take your pick.
In mathematics x = A1*sin(w1*t) * A2*sin(w2*t)
In electronics v = v1*v2 using a transconductance amplifier or something similar.

• geft

#### geft

Joined Dec 8, 2011
19
Thanks, but could you please elaborate on the concept? How does adding or subtracting a frequency make the sine wave pass through the filter?

#### MrChips

Joined Oct 2, 2009
26,811
When you multiply two sine waves, you end up with the sum and difference frequencies.

sin(at)*cos(bt) = [sin(a-b)t + sin(a+b)t]/2

sin(at)*sin(bt) = [cos(a-b)t - cos(a+b)t]/2

So if the input frequency is 600KHz and the local oscillator frequency is 1055kHz, you end up with 455kHz and 1655kHz. Your IF filter is tuned to 455kHz and so you reject the 1655kHz signal. (IF stands for Intermediate Frequency).

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• geft

#### lopoditi

Joined Jul 24, 2011
6
the multiplying sine wave should be 145 kHz

#### Georacer

Joined Nov 25, 2009
5,182
@lopoditi

Here in Homework Help forum, the main goal is to educate the inquirer, not give him a plain result as an answer. If you feel you can contribute, please explain the reasoning behind your answers, and if possible don't give the OP the answer before he tries a bit himself, after he is being given a hint or two.

Thank you.

#### Papabravo

Joined Feb 24, 2006
19,028
the multiplying sine wave should be 145 kHz
It could be but it doesn't have to be because the solutions to the problem are NOT unique. When you use the lower frequency (145 kHz), the sum and the difference are closer together requiring a filter with steeper skirts. When you use the higher frequency (1055 kHz), the sum and the difference are further apart which makes the filtering easier.

#### carmech

Joined Apr 2, 2013
1
please explain this multiplying 2 difference frequencies by drawing 2 freqs one on top
of each other and make notes in the waves that contribute to the resulting frequencies
and show the resulting, GIVE US A VISUAL.

#### Wendy

Joined Mar 24, 2008
22,990
I am approving this post But I don't think you are going to get very far on a 6 year old thread demanding answers

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#### Papabravo

Joined Feb 24, 2006
19,028
please explain this multiplying 2 difference frequencies by drawing 2 freqs one on top
of each other and make notes in the waves that contribute to the resulting frequencies
and show the resulting, GIVE US A VISUAL.

You can do this quire easily in Matlab, or one of the free alternatives like Octave or Scilab. Multiply two sinewaves together and plot over several cycles of the lower frequency. You can even do this in Excel or LibreOffice spreadsheet.

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#### WBahn

Joined Mar 31, 2012
26,937
please explain this multiplying 2 difference frequencies by drawing 2 freqs one on top
of each other and make notes in the waves that contribute to the resulting frequencies
and show the resulting, GIVE US A VISUAL.

This appears to be homework -- so the first step is to show your best attempt to get as far as you can. That gives us a starting point for further discussion.

#### shteii01

Joined Feb 19, 2010
4,644
please explain this multiplying 2 difference frequencies by drawing 2 freqs one on top
of each other and make notes in the waves that contribute to the resulting frequencies
and show the resulting, GIVE US A VISUAL.

That is the job of your instructor.

#### MrAl

Joined Jun 17, 2014
9,360
please explain this multiplying 2 difference frequencies by drawing 2 freqs one on top
of each other and make notes in the waves that contribute to the resulting frequencies
and show the resulting, GIVE US A VISUAL.