In this lab we explored the concept of the input and output impedances of systems. These quantities refer to the "inherent" impedances that any input feeding into, or any load feeding off of, a system interacts with. These internal impedances are im portant because they define how easily maximum amount of potential may be either transferred into, or out of, the system. The three systems whose internal impedances we evaluated were a HP Function Generator (FG), a Sony portable CD player, and a HP 682 5A Programmable Power Supply / Amplifier.
Procedure and Analysis
According to its front panel, the output impedance of the HP Function generator should be 50 Ohms. This specification is for the FG's open-circuit loading condition while activated. The impedance is specified for the FG's on-state simply because the system is very rarely put to any productive use in its off-state, and is specified for the open circuit loading condition because an open circuit is an extremely convenient standard impedance. We confirmed the panel's indication using a Hydra as an ohmm eter, recording a value of 50.28 Ohms. We repeated this confirmation using a different technique by measuring the open circuit output voltage of the FG and then connecting a 46.56 Ohm resistor to the FG and measured the voltage across it. Using the idea that the FG can be modeled with the Thevenin equivalent circuit of an ideal voltage source equal to the FG's open circuit voltage and a resistor (the output impedance of the FG,) the value of the output resistance could then be solved for. Using this method we calculated the output impedance of the FG to be approximately 50.6 Ohms. It should be pointed out that this technique simplifies to creating a voltage divider circuit between the output and load resistors, and thus using a load resistor as close as poss ible to the output impedance will reduce the calculation to dividing the output voltage by two.
The second of these two techniques gives a more accurate value for the output impedance. An ohmmeter operates by applying a small voltage across whatever it is measuring. Since we want to know what the output impedance of the FG is for totally passiv e loads, the interaction between the ohmmeter's applied voltage and the FG's own output voltage will introduce errors.
We next examined the output impedance of our CD player. We first connected the player, via its 'line-out' jack, to a small speaker. The sound output by the speakers was very quiet, and noticeably attenuated all low frequencies (due to the small geomet ric size of the speakers cone.) To try to determine why, we measured the resistance of the speaker, using a Hydra, and the output impedances of both the line-out and headphone terminals, using the Thevenin technique, producing the values shown in Table 1. To use the Thevenin Technique we located a track of music which had an extended repeating chord, and used it as a standard output signal. The oscilloscope was used to determine the voltage values.
|Speaker||Line-Out Terminal||Headphone Terminal|
|8 Ohms||68.4 Ohms||8.9 Ohms|
Since the internal impedance of the line-out terminal is so much higher than that of the speaker, the majority of the output potential will be dropped across the internal impedance, leaving little to drive the speaker, and thus producing the low volume. The impedance of the headphone terminal is much less than that of the line-out, and connecting the speaker to this jack confirmed our assertion, the volume out of the speaker was much greater.
The final system we examined was the HP 6825A Programmable Power Supply / Amplifier. As with the previous two systems, we measured the 6825A's output impedance, but we also measured its input impedance. Both were determined using the Thevenin techniq ue, and the results are listed in Table 2.
|Input Impedance||Output Impedance|
|10.7 kOhms||0.08 Ohms|
As can be seen in the table, the system output impedance is tremendously less than its input. The desirability of a low output impedance was discussed above, but the reasoning between a high input impedance is also fairly obvious. Since an input to the system will form the same sort of voltage divider as we have at the output, a high input impedance is desirable so that the maximum amount of voltage will be dropped inside the system.
Connection of the CD player to the speaker through the 6825A proved the quality of this amplifier, with a significantly louder sound being produced than without. The gain, and thus the final volume of the signal, was variable by adjusting the power leve l of the amplifier (corresponding to the amplifier's DC offset.)
The general desirability of having a high input impedance and low output impedance when designing amplifiers is now self-evident, as well as the problems which can arise when these conditions are not met. This condition is true for not just amplifiers, b ut also for most all systems where one subsystem loads another.