I got an HP3311A function generator. The Sine wave forms below looks pretty bad to my eyes. Is it normal?

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1With what load? What offset voltage? – Elliot Alderson Jul 21 '19 at 22:59
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The load is the probe of an oscilloscope. DC offset is zero. I played a bit with DC offset, it doesn't change the results. – user1596683 Jul 21 '19 at 23:28
2 Answers
As the manual shows, the HP3311A first generates a triangle wave, and then "shapes" it into a sine wave, using the four-segment resistor-diode network shown in Figure 4-2 (on page 4-2). The ~130 Hz waveform in your upper waveform has the classic shape of such a shaper.
The ~1.4 MHz (?) signal in your second trace shows that this shaper has frequency response issues.
Whether this is "good enough" depends on your application. I once needed to generate audio test tones with <70 dB distortion as built-in test for some telecom equipment. I had to go to a great deal of trouble writing DSP code to synthesize waveforms that could meet this specification.
Other applications will have much less stringent requirements. The typical use of this sort of signal generator is to test amplifiers, and measure their overall frequency response. The distortion hardly matters at all in that case.
Your unit may require some tweaking to get down to the 3% THD specified performance. See section 5-26, starting on page 5-11.

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1I'd also like to point out that if audio frequencies are your target, and you're not as concerned about amplitude fidelity as about spectral cleanliness, then any 10€ sound card will perform better. Of course, you can't do 1.4 MHz with a soundcard... – Marcus Müller Jul 22 '19 at 01:59
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Yes, I have been using various beeping frequencies from the laptop as calibration signals. The waveform looks much better than this. – user1596683 Jul 22 '19 at 15:00
The main problem is the Triangle Amplitude that drives the diode shaper. If you fix the triangle amplitude to obtain +/- 2V, then the diode shaper 3x +/- 0.6Vp~ = 1.8Vp which compresses the signal to approx 80% to 88% that results in 1% to 3% THD.
Your scope indicates only +/-450mV rather than my estimate of +/- 1.676 based on my fourier analysis converting a triangle to sine with <3% dist. = -31 dB for 3f. by reducing harmonics by 6dB.
The 1.2MHz amplitude problems should also not be too difficult to trace the fault by following the service manual and calibrating the test points for correct supply voltage and bias voltage.
Other
Your scope seems to be struggling with blanking the retrace at 200ns/div, which is visible.

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The amplitude is adjustable on the instrument. I did not pay much attention on the amplitude other than have it small enough to avoid potential distortions. – user1596683 Jul 22 '19 at 14:48
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Yes, my Tek 7904 is struggling with blanking. Yet another thing to fix, lol. – user1596683 Jul 22 '19 at 14:56
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NO the source must be +/-2V to create the sine wave. Then a variable atten/gain amp follows. – Tony Stewart EE75 Jul 22 '19 at 19:34
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YOu can easily fix it if you do as said. Fix the +/-2V triangle amplitude – Tony Stewart EE75 Jul 22 '19 at 20:36