Agilent Technologies E1441A Floating Signal Generators, Attributes of AC Signals, Appendix C

Floating Signal Generators

Many applications require a test signal which is isolated from earth ground for connection to powered circuits, to avoid ground loops, or to minimize other common mode noise. A floating signal generator such as the Agilent E1441A has both sides of the output BNC connector isolated from chassis (earth) ground. As shown in the figure below, any voltage difference between the two ground reference points (Vground) causes a current to flow through the function generator's output common lead. This can cause errors such as noise and offset voltage (usually power- line frequency related), which are added to the output voltage.

The best way to eliminate ground loops is to maintain the function generator's isolation from earth ground. The function generator's isolation impedance will be reduced as the frequency of the Vground source increases due to low-to-earth capacitance Cle (approximately 4000 pF for the Agilent E1441A). If the function generator must be earth-referenced, be sure to connect it (and the load) to the same common ground point. This will reduce or eliminate the voltage difference between devices. Also, make sure the function generator and load are connected to the same electrical outlet if possible.

Attributes of AC Signals

The most common ac signal is the sine wave. In fact, all periodic waveshapes are composed of sine waves of varying frequency, amplitude, and phase added together. The individual sine waves are harmonically related to each other — that is to say, the sine wave frequencies are integer multiples of the lowest (or fundamental) frequency of the waveform. Unlike dc signals, the amplitude of ac waveforms varies with time as shown in the following figure.

A sine wave can be uniquely described by any of the parameters indicated -- the peak-to-peak value, or RMS value, and its period (T) or frequency (1/T).

The magnitude of a sine wave can be described by the RMS value (effective heating value), the peak-to-peak value (2 x zero-to-peak), or the average value. Each value conveys information about the sine wave. The table below shows several common waveforms with their respective peak and RMS values.

Each waveshape exhibits a zero-to-peak value of "V" volts. Crest factor refers to the ratio of the peak-to-RMS value of the waveform.

RMS The RMS value is the only measured amplitude characteristic of a waveform that does not depend on waveshape. Therefore, the RMS value is the most useful way to specify ac signal amplitudes. The RMS value (or equivalent heating value) specifies the ability of the ac signal to deliver power to a resistive load (heat). The RMS value is equal to the dc value which produces the same amount of heat as the ac waveform when connected to the same resistive load.

For a dc voltage, this heat is directly proportional to the amount of power dissipated in the resistance. For an ac voltage, the heat in a resistive load is proportional to the average of the instantaneous power dissipated in the resistance. This has meaning only for periodic signals. The RMS value of a periodic waveform can be obtained by taking the dc values at each point along one complete cycle, squaring the values at each point, finding the average value of the squared terms, and taking the square-root of the average value. This method leads to the RMS value of the waveform regardless of the signal shape.

Peak-to-Peak and Peak Value The zero-to-peak value is the maximum positive voltage of a waveform. Likewise, the peak-to-peak value is the magnitude of the voltage from the maximum positive voltage to the most negative voltage peak. The peak or peak-to-peak amplitude of a complex ac waveform does not necessarily correlate to the RMS heating value of the signal. When the specific waveform is known, you can apply a correction factor to convert peak or peak-to- peak values to the correct RMS value for the waveform.

Appendix C Agilent E1441A Function Generator Tutorial 157