# Calculate total harmonic distortion

I have the following problem.

MY ATTEMPT

I found the formula for the total harmonic distortion to be this:

$$\THD = \frac{\sqrt{V_2^2+V_3^2+V_4^2+V_5^2+...}}{V_1} \$$, where the subscript denotes the harmonic.

Looking at the spectrum above, it seems like I'm supposed to make the following conclusions: V1 = 18.9241, V2 = -67.363, V3 = -8.5635, V4 = -61.8046, V5 = -13.3634.

Inserting these values in the formula gives me a result of $$\THD = 4.90 \$$ which doesn't seem reasonable at all, I must be doing something wrong. I'm also unsure of where I'm supposed to use the information about the forward voltage of the diode.

I hope someone can help me or clarify things for me.

The amplitude distortion plot you showed is in dB, dBV specifically (dB's relative to 1 V). So you need to take those dB values and covert them into volts before putting them into your formula.

For example, -67.363 dBV is 0.000428 V (RMS) (using an on-line calculator).

You should be able to take it from here.

• Also worth noting that the fundamental frequency (= the desired output) should not be included when calculating distortion.
– jpa
May 18, 2020 at 6:00
• @SteveSh - Okay, I am now converting all the voltages from dBV to V. V1 = 8.835V, V2 = 0.000428V, V3 = 0.3731, V4 = 0,000812 V, V5 = 0,2147 V. So far so good, but where do I go from here? Do I just plug these number into the equation, or do I need to take the diode into consideration as well?
– Carl
May 18, 2020 at 8:05
• I would have to see the schematic. But if the specan levels are after the diode, then you don't need to do anything else to account for the diode. May 18, 2020 at 12:21
• @SteveSh - Sadly, there were no schematic included for this problem but I still think I have to take into account the diode. I just have to figure out how.
– Carl
May 18, 2020 at 17:13