An Audio Preamplifier

Fig. 1 shows a typical single-ended inverting audio amplifier that might be used in low cost amplifiers for medium level inputs such as an electret microphone or as a hi-z headset amplifier. Depending on the quality of the op-amp utilized the circuit is capable of low harmonic distorsion (better than -60db) and depending on the external components and op-amp bandwidth we could obtain 20 to 20KHZ response within +/- 2 db or better flatness.

We present this amplifier to use as an example of analyzing gain and phase with a equation based method using typical math solving software, e.g., Mathcad ™ or Matlab ™.

The closed loop gain can be easily determined using our previous article on the inverting amplifier as

G = - Zf / Zin

Working in the frequency domain we can define the quantity s as

s = j *2*Pi*f

where j is the square-root of -1, Pi is 3.14159…, and f is the frequency of interest.

To simplify the equations we will define the following quantities (refer to Fig. )

Zcb = 1 / (s*Cb)

Zca = 1 / (s*Ca)

which are the impedances of the capacitors Ca and Cb. Then the net parallel impedance of the feedback loop is

Zf = Rb*Zcb / (Rb + Zcb)



and Zin = Ra + Zca

So we can now calculate the value of G versus frequency using one of the math software packages that will handle the complex number calculations.

Now in order to get a gain versus frequency response in practical numerical values that can be plotted in the traditional manner, that is voltage decibels vs. positive frequency, we first find the absolute value of the gain function (again using a software package) as

Gabs = G

Then the gain function can be calculated vs. frequency in terms of decibels as

Gdb = 20* log (Gabs)

and we can determine phase shift vs. frequency if we want to from

P = arg (G)

where arg is called the argument of the complex value of G (vs. frequency) and yields the phase vs. frequency. We will probably want to convert the phase computed above which is in the units of radians to the units of degrees and we would use the following equation:

Pdeg = 180*P / Pi

Using a software package the values computed at each frequency increment can be plotted vs. frequency and the cut-off frequencies, flatness, and phase can be determined from the plot or data generated.

An example of a typical design for a gain of ten amplifier would use a quality op-amp which is available from a number of reputable manufacturers, and a positive and negative supply voltages of at least +/- 3 volts or higher if a larger output signal is needed. The following components are suggested for the gain of ten preamp:

Ra = 1K
Ca = 22MFD
Rb = 10K
Cb = 470PF
I simulated this circuit with a Linear Technology ™ LTC6241 op-amp with excellent results, but as I mentioned a number of quality op-amps that would work are available from a number manufacturers.