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I just got a very old function generator (I can't even tell the manufacture and the model number) to produce sine wave. I open it and see a big module label video amplifier. The function generator come with a digital switch to choose different level of attenuation. I look everywhere inside and didn't see any module for attenuation. I wonder if the amplifier is really for built to attenuate the signal? Basically are amplifier and attenuator of similar circuit design?

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It is extremely unlikely that the sole purpose of the amplifier is to provide attenuation. Attenuation can be achieved with a bank of resistors that will provide more accuracy, higher bandwidth, lower noise and better reliability than an amplifier using active devices like vacuum tubes (if the generator is that old) or transistors. Resistors also don't require any power. The most common design for signal generators is to have a basic oscillator to provide the signal followed by a power amplifier designed to deliver the maximum desired output power. A resistive attenuator at the amplifier output than is used to select the desired output level and provide the desired output impedance (usually 50 or 600 ohms). At full power, the attenuator would be switched out entirely. As for the digital switch, could you provide a more detailed description. It's possible that the attenuator resistors are built into the switch.

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Basically are amplifier and attenuator of similar circuit design?

No, an amplifier increases the power of a signal while an attenuator decreases the power of a signal.

In order to increase power, the amplifier circuit must have a power supply, i.e., it is an active circuit.

Now, keep in mind that an active circuit can have, for example, a (magnitude) voltage gain less than 1, e.g., a common-collector amplifier. However, the common-collector amplifier can have substantial power gain since it has relatively high input impedance and relatively low output impedance.

An attenuator circuit can be passive. For example, a resistive voltage divider converts some of the input signal power to heat.

Note that while an ideal transformer can give voltage gain or current gain, it cannot give both; the power out equals the power in.

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