Amplifier pass-band

In most amplifiers applications we want fidelity of amplification (=>output wave shape identical to the input shape form). If the input signal is non-sinusoidal (the principles of Fourier analysis show that such signal consist of broad spectrum of harmonically related frequencies) to achieve undistorted output all component frequencies (to 3 - 5 harmonics of repetition frequency) must be equally amplified in magnitude.

Unequal gain for the frequency components causes (gain - frequency curve and phase - frequency curve)) distortion.

In middle-frequency range the gain and phase angle are reasonable constant => circuits reactances have negligible effect (series-capacitive reactances approximate short circuits, all shunt-capacitive reactances appear as effective open circuits)

In high-frequency range shunt capacitance (result of the internal transistor capacitance) reduces the load impedance and output voltage.

In low-frequency range the series capacitance increase in reactance and progressively cause a drop in the response with falling frequency.

The amplifier bandwidth BW=f_H0-f_L0since the low frequency limit BW can be extended to zero frequency, the high-frequency limit restricts the amplifier bandwidth.
 
 Fig. 3-85

Gain-frequency curve; Phase-frequency curve Fig. 3-85a

Gain versus frequency curves driven in logarithmic scale are known as Bode plots => we can employ straight-line approximation to obtain the performance characteristic corner frequency at which asymptotes of the dB curves intersect. => correction for curve in corner frequency (10 log2=3dB).

Gain-frequencies curves in dB being additive. (The gain of 2-stage identical amplifier fall at -40dB per frequency decade (12 dB per octave), 3-stage circuits will have a gain curve that falls at -60dB per decade. The phase angle will be multiplied by the number of stages +-90^o and at extreme frequency in n-stage amplifier => critical condition for oscillation. When stages of the amplifier are cascaded the bandwidth is reduced.
 
 

Fig. 3-85b Response curves (3 stages amplifier) from Bode asymptotes.

Feedback

Black box width feedback (voltage) illustrates the sampling by the b (beta) network and reverse transmissions of signal in feedback system. (=> giving on output bU₂ => is subtracted from the voltage U₁ at the mixing point, to yield the error signal U_D.
 

Fig. 3-80 Principle of the feed back

Open-loop gain A_D- internal gain of the amplifier.
In sampling of the input voltage bU₂ (on fig. beta*U₂)

Closed-loop gain A= A_D/(1+bA_D)~1/b.
 

Output sampling:

Output resistance in:

voltage feedback	current feedback
R'0=R0/(1+bAD)	R'0=R0(1+bAD)

 

Fig. 3-81 Output sampling

 

Effect of feedback on input resistance:
 

Seriesinput:	Shunt input:
R'i=Ri(1+bAD)	R'i=Ri/(1+bAD)

 

Fig. 3-82 Effect of feedback on input resistance

Applications examples of op amp

Inverting op amp, non-inverting op amp and the unity-gain buffer
 
 

Fig. 3-83 Operational amplifier: Inverting (A=Uo/Ui= -Zf/Zi) Noninverting (A~1+Zf/Zi) Current-voltage converter

The integration operation amplifier (in fig (a) above, if Z_f is a capacitance  will perform mathematical operation of integration on the input signal). By considering property of the integration operation amplifier the Miller effect can be explained as increasing equivalent input capacitance C'=(1+A_D)C and so a very large time constant circuits can be achieved. Example of such a circuit see active integrator called "charge sensitive amplifier"
 

Fig. 3-84 Operational amplifier Inverting (A=Uo/Ui= -Rf/Ri) Input and output impedance Noninverting conection (A~1+Rf/Ri) - for Rf=0 and Ri=inf is gain ~1. An amplifier of unity gain is sometimes called a buffer or follower.

The application of negative feedback to amplifiers is effective in increasing the amplifier bandwidth. In general, instability of the voltage feedback never differs as much as 180^o from its middle-range => reduce by corrective RC circuits in 1 stage. The compensation network seriously reduces the amplifier bandwidth.
 

Fig. 3-85c Constant gain-band-width product with 15-dB feedback => increasing the amplifier bandwidth.

Monolithic construction, with a complete amplifier integrated into tiny silicon chip, leads very small size, balancing of temperature effects, reduced cost, and improved reliability by elimination of much interconnecting wiring.

By addition of negative feedback to a high-gain (A>5000) integrated amplifier => operational amplifier ("op-amp"). This circuits closely approaches an ideal package of gain, with high input resistance and low output resistance.

Use of negative feedback sacrifices gain, reduce distortion, improve stability of gain, alter frequency response and modify input and output impedance.
 

Fig. 3-86 Example of compensation of 709 operational amplifier => reducing by corrective RC circuits the amplifier bandwidth.	Fig. 3-87 Gain and phase margins after correcting with RC circuits.

Capacitance of the pn-junction

When a pn-junction is under reverse voltage U_D (case of semiconductor detector) the transition region is depleted of mobile charges (=> More mobile charge is removed and the depleted region increases whit increasing U_D) and takes on the properties of a dielectric, with only fixed charges present.

The dynamic transition capacitance depends on r.m.s. of applied voltage (U_B+U_D)~U_D, where U_B - barrier potential of junction, U_D - applied outside voltage:

To make charge response independent of variance in detector capacitance is necessary use active integrator called "charge sensitive amplifier"
 

Fig. 3-84 Active integrator called "charge sensitive amplifier". The gain AQ ~ 1/Cf depnds on the feedback capacitance Cf and did not depnds on capacitance Cdet of the semiconductor detector.