An amplifier may be characterized using metrics such as gain, power, class, phase shift, transient response, frequency response, noise, and distortion. This is a complex topic for which many books have been written. In this article we will focus on distortion using a pure sinusoid signal and a spectrum analyzer to look for undesirable harmonics.
Historically, the spectrum analyzer was an expensive piece of test equipment. It was out of reach for the hobbyist and even most students. That has changed with the advent of low-cost digital test equipment. For example, the Digilent Analog Discovery device featured in this article encapsulates what was traditionally a workbench full of expensive test equipment. This includes a spectrum analyzer that will measure audio signals all the way up to radio frequencies.
The spectrum analyzer is a useful measurement tool for amplifier analysis. However, for meaningful results we must “feed” the amplifier with a pure sinusoid signal. The ideal amplifier will act as a “wire with gain” providing a faithful replica of the original. Real world amplifiers will add noise, harmonics, and even intermodulation with the power supply ripple frequency or a second tone should you chose to perform a two-tone test.
In this article we will discover the performance of the common emitter transistor amplifier as shown in Figure 1 and schematically as Figure 2. The test will be conducted using a 1 kHz tone generated from the Wien bridge oscillator as described in this previous post. This simple oscillator has remarkably spectral purity which is essential for analyzing amplifier performance. In fact, for the single tone that it produces, the Wien bridge has better performance than many commercially available signal generators.
Figure 1: Picture of a common emitter transistor amplifier with a Wien bridge oscillator in the background.
Figure 2: Multisim live schematic of the transistor circuit. Click on the schematic to view the simulation.
Common Emitter Amplifier
The Common Emitter (CE) transistor amplifier shown in Figures 1 and 2 is a classic design with degenerative feedback via resistor R5. It features fixed bias via resistors R2 and R3 with capacitive input coupling via C1. The output is also capacitively coupled via C2 to the load resistor R6.
From an AC analysis resistors R4 and R6 are in parallel. The resulting amplifier gain is approximated as
Gain \approx \dfrac{10\ k\Omega \ || \ 10 \ k \Omega} {470 \ \Omega}
Results
Two experiments were conducted to evaluate the amplifier. The first is a small signal test. The second is a larger signal test set with the R1 gain set to the onset of clipping.
The results of the first test are shown in Figures 3, 4, and 5:
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Figure 3 presents the time-domain (oscilloscope) representation of the input (orange) and output signal (blue). This demonstrates that the amplifier gain is approximately 10 and has the expected 180° phase shift associated with the common emitter amplifier. No waveshape distortion is present, although channel 1 does exhibit noise.
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Figure 4 presents the spectrum of the input signal. The waveform shows a pure sinusoid with a -22 dBV level and a noise floor at approximately -90 dBV. Please see this earlier introduction to the Wien bridge oscillator article for more information about the signal source.
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Figure 5 presents the amplifier’s output spectrum. The output is relatively clean with 2nd order harmonics at 2, 4, and 6 kHz. On the far left we can also see a small 60 or 120 Hz component. This is likely line hum picked up from the DC power supply.
Figure 3: Oscilloscope representation of the amplifier input (orange) and output (blue).
Figure 4: Spectrum of the amplifier’s input signal showing a pure sinusoid at approximately 1 kHz.
Figure 5: Spectrum of the amplifier’s output signal showing the 1 kHz fundamental and even harmonics at 2, 4, and 6 kHz.
Tech Tip: The perfect amplifier is a unicorn – there is no such thing as a “wire with gain.” Real world amplifiers will add noise to the signal. In audio amplifier this manifests as a hiss sound plus hum at the line frequency. Amplifiers can also add harmonics. As shown in Figure 4, the simple transistor amplifier added spectral components that were not present in the Figure 3 input signal.
The results of the second test are captured in Figures 6 and 7. For this test the R1 “volume control” was increased until the output displayed soft clipping as shown in Figure 6. Close visual inspection will show that the tops of the blue output waveform have been flattened.
The spectrum for the overdriven amplifier is shown in Figure 7. The amplifier’s output has strong even harmonics at 2, 4, 6, and 8 kHz. It also has strong odd harmonics at 3, 5, 7, and 9 kHz.
Figure 6: Time-domain signal showing the onset of clipping for the blue output signal.
Figure 7: The overdriven amplifier has strong even and odd harmonics.
Tech Tip: Be mindful of your spectrum analyzer attenuation settings. An overdriven spectrum amplifier will display garbage across the spectrum. Attenuator setting should be one of the first things to check if there is doubt about a signal’s integrity.
Conclusion
An amplifier may be characterized by its spectrum. For these tests we inject the best – spectrally pure – sinusoid available. We then used a spectrum analyzer to monitor the amplifier output. The presence of and nature of the amplifier’s distortion is readily apparent.
Please give this method a try. Years ago, it would have been difficult due to limited test equipment capabilities. Today, it you are a student, chances are very high that the classroom oscilloscopes have a built-in spectrum analyzer capability. Look for the Fast Fourier Transform (FFT) function under the math menu.
Best Wishes,
APDahlen