Essay: AC characteristics

2.4 AC characteristics
For small signal sinusoidal (ac) applications, one has to know the ac characteristics such as frequency response and slew rate.
Frequency Response of an OP-Amp
Ideally an open loop op-amp has infinite Bandwidth. It means that, if its A0L = 90dB with dc signal its gain should remain the same 90dB through audio and on to high frequencies. But with practical op-amp ,gain decreases (rolls off) at higher frequencies.
High frequency of an op-amp with single corner frequency
The reason for the above is that there must be a capacitance component in the equivalent circuit of op-amp. This capacitance is due to the physical characteristics of device (BJT or FET) used and internal construction of op-amp. For the op-amp with one corner frequency all the capacitor effects can be represented by a single capacitor C as in diagram.
Due to single R0C, there is one pole and obviously one –20dB/ decade rolls off comes into effect. The open loop gain of an op-amp with only one comer frequency is obtained from the figure as
Where, f1 – comer frequency of the op-amp.
The magnitude and phase angle of the open loop voltage gain can be written as
The magnitude and phase characteristics as shown in figure.
Open loop magnitude characteristics in semi-log paper
From the graph,
1. For frequency f <fi, the magnitude of the gain is 20 log AOL in dB.
2.For f=f1 the gain is 3 dB down from the dc value of AOL in dB. This frequency f1 is called corner frequency.
3.For f >> f1, the gain rolls off at the rate of –20 dB/decade (or) 6dB/octave.
Phase Characteristics for an op-amp with single break frequency
From the phase Characteristics the phase angle is zero at frequency ƒ = 0. At f1, phase angle is –45°(lagging) and at infinite frequency phase angle is -90°. This shows that a maximum of 90°phase change can occur in an op-amp with a single capacitor.
The voltage transfer function in s-domain can be written as
Due to a number of RC pole pairs, there will be a number of different break frequencies. The transfer function of an op-amp with 3 different break frequencies can be assumed as
0 ≥ f1 < f2< f3
with 0 < ω1 < ω2 < ω3
Approximation of open loop gain Vs frequency curve is shown in Fig.
Approximation of open loop gain Vs frequency curve
Approximation of open loop gain Vs frequency curve is shown in the figure. For frequencies from 0 Hz to 200 KHz, open loop frequency response is constant (90 db).
From 200 kHz – 2MHz – gain drops from 90 dB to –70 dB which is at a -20 dB/decade. From 2 MHz – 20 MHz – the roll off rate is –40 dB/decade.
As frequencies increase, cascading effect of RC pairs (poles) come into effect and roll-off rate increases successively by -20 dB/decade at each corner frequency.
2.5 Differential amplifier
CMRR:
It is the ratio of the differential mode voltage gain Adm to common mode voltage gain Acm expressed in terms of decibels.
BJT – emitter coupled differential amplifier:
The open circuit voltage gain of an op-amp should be large as possible and this is achieved by cascading gain stages. Thus to increase Ad, RC must be as high as possible. But, there are limitations to select maximum value of RC such as:
(i)For large RC, the quiescent drop is more, Hence, higher biasing voltage is necessary to maintain the quiescent collector current.
(ii)Higher value of RC requires a large chip area. Hence, it is not possible to increase the value of RC beyond a particular limit.
The current mirror circuit has very low d.c. resistance (few kilo ohms) and higher a.c. resistance. Hence, the current mirror circuit can be used as a collector load instead of RC. Such a load is called an active load. The quiescent voltage across the current mirror is the traction of the supply voltage. This eliminates the need of high biasing supply voltage.
It basically acts as a current source and provides large AC resistance. The differential amplifier using a current mirror as an active load is shown in the figure.
Differential amplifier as an active load
Under the quiescent conditions, VS1 = VS2 = 0. As Q1 and Q2 are matched transistors hence I1 =I2 = IEE/2, where base currents of Q1 and Q2 are neglected. The transistors Q3 and Q4 form a current repeater, load current IL entering the next stage is,
However, when VS1 is increased over VS2, the current I1 increases whereas I2 decreases. Therefore, I1+I2 = IEE (constant). Also, the current I always remains equal to I1 due to the current mirror action.
Thus, the active load provides very high a.c. resistance and hence high differential voltage gain. Thus, as Ad becomes high, CMRR gets improved.
Different Configurations of Differential Amplifier:
The differential amplifier can be used in four configurations:
(i)Dual input, balanced output differential amplifier.
(ii)Dual input, unbalanced output differential amplifier.
(iii)Single input, balanced output differential amplifier.
(iv)Single input, unbalanced output differential amplifier.
(a) Dual input balanced output
(b) Dual input unbalanced output
(c) Single input balanced output
(d) Single input unbalanced output
Two transistors in common emitter configuration is used in differential amplifier. If output is taken between the two collectors it is called balanced output or double ended output.
If the output is taken between one collector with respect to ground, it is called unbalanced output or single ended output. If the signal is given to both the input terminals, it is called dual input. If the signal is given to only one input terminal and other terminal is grounded, it is called single input or single ended input.
Out of these four configurations, the dual input balanced output is the basic differential amplifier configuration. This is shown in figure.(a). The dual input, unbalanced output differential amplifier is shown in the Figure.(b).
The single input, balanced output differential amplifier is shown in the Figure.(c). The single input, unbalanced output differential amplifier is shown in the figure. (d).