# VCA.MTH.3

Lesson Summary

Recognize the logarithmic relationship in dB and its difference between linear relationships.

Vocabulary

Amplitude -  The maximum absolute value of the signal. Designated by an uppercase A.

Pascal - the SI derived unit of pressure. Designated by Pa.

Decibel - A logarithmic unit used to express the ratio between two values of a physical quantity. Decibel is commonly used in acoustics as a unit of sound pressure referencing a pressure of 20 micropascals. Designated by a dB.

Inverse-square law - A physical law that states an intensity is inversely related to the square of the distance from the source's point of origin.  In acoustics a common example is the doubling of distance from any point of sound origin drops the sound level by 6dB, regardless of the original sound's dB level.  Meaning if you double your distance from a rock concert at 100dB the sound drops by 6dB, if you quadruple your distance the sound drops by 12dB etc.  This relationship would be the same at any original dB.

Exercise

Experiment with the VCA IN of the Werkstatt

Materials
 3.3kΩ, 10kΩ, 680kΩ & 1MΩ Resistors 1 x 10kΩ Potentiometer Jumper Cables 1 x AA Battery Holder
Hardware

We will be adding a volume knob to work with our Werkstatt.  This knob will change the dB output of of Werkstatt.  First we will need to match the settings to Figure 1.   This will give us a constant Sawtooth wave to experiment with.

Figure 1. Sawtooth wave VCA MODE ON

When our Werkstatt VCA is set to to MODE ON we get a constant tone.  This also means that our VCA IN pin can accept a voltage from -2.5 to +2.5 V.  To create have volume control we will need to use a negative voltage.  To do this we simply connect our battery backwards.  A battery pack has two leads, one red (positive) and one black (ground).  By simply swapping these two leads we will be able to get a -3V from our two AA batteries.  We then pass this -3V through our 4.7kΩ resistor to have control over the Werkstatt's volume.  Observe Figure 2 for a detailed visual diagram.

Figure 2. VCA IN with 4.7kΩ resistor

Compare and contrast the volume changes with a 3.3kΩ resistor and a 6.8kΩ resistor.  Notice how as resistance is lowered so is our volume. Observe Figures 3 and 4 to see the difference in linear and logarithmic relationships.

Figure 3 shows us how voltage and resistance have a linear relationship.  As resistance increases the less of the -2.5V is allowed to pass through and we get closer to 0V.

Figure 3. Linear relationship between voltage and resistance

In contrast Figure 4 shows the relationship of applying -2.5V to our VCA IN has on dB output.  Since dB must be in reference to something these values are in reference to 20 micro Pascals (µP), or the threshold of human hearing.  The Werkstatt does not have a built-in speaker so the dB output values are based on the maximum headphone values.

Figure 4. Voltage and dB output of VCA IN

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