Difference effect filter in before and after amplifier

When you amplify something, you are increasing the power. If you look at the cost of components, it will cost you less to filter a "pre-amped" signal.

Also, why would you want to amplify the "dirty" parts of a signal?

Clean it up, then amplify.

The answer is yes in ideal circuit theory and the approximation to it that we call "The Real World".

Consider an ideal RC low-pass filter. The open-circuit output voltage, due to an input voltage \$V_s\$ is

$$V_{o} = V_s \frac{1}{1 + j \omega RC}$$

However, if one connects a load impedance \$Z_L\$ to the output of this filter, the loaded output voltage is

$$V_{ol} = V_s \frac{Z_L}{R + Z_L}\frac{1}{1 + j\omega \left( R||Z_L\right)C}$$

Thus, the DC gain and frequency response of our low-pass filter depends on the load \$Z_L\$

However, if there is a good amplifier (high input impedance, low output impedance) between the low-pass filter and the load, the DC gain and frequency response will effectively be independent of \$Z_L\$.

There are other reasons you might want the filter before the amplifier rather than after. For example:

• With the low-pass filter before the amplifier, the amplifier is not required to needlessly amplify frequencies well above the corner frequency.
• If the low-pass filter is after the amplifier, the power delivered to the load must pass through the filter.

and which one is good for PC audio amplifier?

Without more details of your application, it isn't clear what the 'good' is.

Ideally there is no difference. If the filter is just a mathematical thing that you put in a signal processing chain, in this case its position it's irrelevant.

Luckily we live in the real world, so math has its own limits.

If you are interested only in the low portion of the spectrum of your signal, then why would you amplify it all? Amplifying costs power, and that's something you generally want to save. Moreover a filter after an amplifier should handle more powerful (aka amplified) signals, so it will need "bigger", more expensive components. Processing a signal before it gets amplified is not the golden rule, there are tons of situations where the opposite is true, but I've got the feeling that you want to build a set of loudspeakers thus your input is line signal, while your output is a somewhat powerful signal meant to drive the speakers. If that's the case you will need a LP filter on your input unless you want any kind of signal messing around in your circuit. If you don't use a LP and your amplifier has a somewhat wide band it can amplify some high frequency signal which you can't even hear, wasting a lot of power... For nothing.