7. BJT_JFET Frequency Response

Sem I 0809/rosdiyana

Chapter 7:Chapter 7:Chapter 7:Chapter 7:

BJTBJT

Frequency ResponseFrequency Response

Contents• Logarithm and dB • Low frequency analysis-Bode plot• Low frequency response-BJT amplifiers• Miller effect capacitance• High frequency response-BJT amplifiers• Multistage frequency effects• Square wave testing

Logarithms

alog x,ba

:function clogarithmi a of variablesebetween th iprelationsh

bx

alog x:logarithmCommon 10

alogy : logarithm Natural e

a2.3logalog 10e

The two are related by:

Formula 9.1

Formula 9.2

Formula 9.3

Formula 9.4

blogalogablog

blogb

1log

blogalogb

alog

01log

101010

1010

101010

10

Formula 9.5

Formula 9.6

Formula 9.7

Formula 9.8

Logarithms

Semilog graph paper.

Identifying the numerical values of the tic marks on a log scale.

• Vertical scale- linear scale with equal divisions• The distance from log10 1=0 to log10 2 is 30% of the span.• Important to note the resulting numerical value and the spacing, since

plots will typically only have the tic marks.• Plotting a function on a log scale can change the general appearance

of the waveform as compared to a plot on a linear scale.• Straight line plot on a linear scale can develop a curve on a log scale.• Nonlinear plot on a linear scale can take on the appearance of a

straight line on a log plot.

Semilog

Decibels

ndBdBdBdBdB

1

210dB

600Ω

210dBm

1

210dB

1

210

G........GGGG

(dB) V

V20logG

1mW

P10logG

bel 1 dB *10*

(dB) P

P10logG

(bel) P

PlogG

321T

Formula 9.9

Formula 9.10

Formula 9.11

Formula 9.12

Formula 9.15

• Term decibel-the fact that power and audio levels are related on a logarithmic basis.

• P1, P2 – power levels• Bel-too large unit of measurement for practical

purpose.• The terminal rating of electronic communication

equipment is commonly in decibels.• Decibels- is a measure of the difference in magnitude

between two power levels.• Advantages of the logarithmic relationship, it can be

applied to cascade stages.

Decibels

Gain versus Frequency

Low Frequency Analysis

0ΩπfC2

1XC

RC combination that will define a low-cutoff frequency.

ΩCπ(0)2

1

πfC2

1XC

RC circuit at f = 0 Hz.

RC circuit at very high frequencies.

Low-frequency response for the RC circuit

• A low frequency, the reactance of the capacitive becomes very large, so a significant portion of a signal dropped across them.

• Then as the frequency approaches zero or at dc, the capacitive reactance approach infinity or become an open circuit.

• As the frequency increases, the capacitive reactance decreases andmore of the input voltage appears across the output terminals.

Low Frequency Analysis

Low Frequency Analysis

Bode plot for the low-frequency region.

1. Determine the break frequency.

2. Plot f1 point on the log scale.

3. Draw straight-line segment (slope) from f1 point to -20dB at linear scale.

4. In the same figure, draw straight-line for the condition of 0dB.

5. When f= f1 , there is a 3dB drop from the mid-band level. Plot this point.

6. Find the 3dB point corresponding to f1 and sketch the curve.

RCf

2

11

Low Frequency Analysis

2

3

4

56

Low Frequency Response – BJT Amplifier

At low frequencies Coupling capacitors (Cs, CC) and Bypass capacitors (CE) will have capacitive reactance (XC) that affect the circuit impedances.

Coupling Capacitor - CS

sisLs )CR(R2

1f

Determining the effect of CS on the low-frequency response.

Cutoff frequency:

Voltage Vi:si

sii RR

VRV

βre||R||RR 21i

Localized ac equivalent for CS.

Coupling Capacitor - CS

Coupling Capacitor - CC

CLoLC )CRR(2

1f

π

Cutoff frequency:

Determining the effect of CC on the low-frequency response.

oCo r||RR

Localized ac equivalent for CC with Vi = 0 V.

Coupling Capacitor - CC

Bypass Capacitor - CE

EeL CR2

1f

E π

Determining the effect of CE on the low-frequency response.

Cutoff frequency:

)rβ

R(||RR e

sEe

21ss R||R||RR

Localized ac equivalent of CE.

Bypass Capacitor - CE

Example

a. Determine the lower cutoff freq. for the network of Fig. 1 using the following parameters:

Cs = 10μF, CE = 20μF, Cc = 1μF

Rs = 1KΩ, R1= 40KΩ, R2 = 10KΩ,

RE = 2kΩ, Rc = 4kΩ, RL = 2.2KΩ,

β = 100, r0 = ∞Ω, Vcc = 20V

b. Sketch the frequency response using a Bode plot

Bode Plot of Low Frequency Response – BJT Amplifier

The Bode plot indicates that each capacitor may have a different cutoff frequency.

It is the device that has the highest of the low cutoff frequency (fL) that dominates the overall frequency response of the amplifier (fLE).

Roll-off of Gain in the Bode Plot

The Bode plot not only indicates the cutoff frequencies of the various capacitors it also indicates the amount of attenuation (loss in gain) at these frequencies.

The amount of attenuation is sometimes referred to as roll-off.

The roll-off is described as dB loss-per-octave or dB loss-per-decade.

Roll-off

-dB/Decade

-dB/Decade refers to the attenuation for every 10-fold change in frequency. For Low Frequency Response attenuations it refers to the loss in gain from the lower cutoff frequency to a frequency 1/10th the lower cutoff frequency.

-dB/Octave

-dB/Octave refers to the attenuation for every 2-fold change in frequency.For Low Frequency Response attenuations it refers to the loss in gain from the lower cutoff frequency to a frequency 1/2 the lower cutoff frequency.

Miller Effect Capacitance

Any P-N junction can develop capacitance. This was mentioned in the chapter on diodes.

In a BJT amplifier this capacitance becomes noticeable between: the Base-Collector junction at high frequencies in CE BJT amplifier configurations and the Gate-Drain junction at high frequencies in CS FET amplifier configurations.

It is called the Miller Capacitance. It effects the input and output circuits.

Miller Input Capacitance (CMi)

It can be calculated: [Formula 9.42]

Note that the amount of Miller Capacitance is dependent on interelectrode capacitance from input to output (Cf) and the gain

(Av).

fMi CAv)(1C

Miller Output Capacitance (CMo)

It can be calculated: [Formula 9.43]

If the gain (Av) is considerably greater than 1:

[Formula 9.44]

fMo )CAv

1(1C

fMo CC

High-Frequency Response – BJT Amplifiers

Capacitances that will affect the high-frequency response:

• Cbe, Cbc, Cce – internal capacitances • Cwi, Cwo – wiring capacitances • CS, CC – coupling capacitors • CE – bypass capacitor

High-frequency ac equivalent model for the network

High-Frequency Response – BJT Amplifiers

fvMi )CA(1C fv

Mo )CA

1(1C

Thevenin equivalent circuit for the input circuits.

Thevenin equivalent circuits for the output circuits.

High-Frequency Response – BJT Amplifiers

bcvbeWi

MibeWi

CACC

CCC

)1(

MoceWo CCC

High-Frequency Cutoff

iThiHi CR2

1f

π

Cut-off frequency for input circuits:

Cut-off frequency for output circuits:

oThoHo CR2

1f

π

Total Amplifier Frequency Response

• fL – produce by coupling & bypass capacitor at low frequency.

• fH – produce by interelectrode capacitance at high frequency

• Dominant frequencies are referred to as the lower critical frequency fL and the upper critical frequency fH

• fH and fL are sometimes called the half-power frequencies.

Example• Use the network for high frequency response with the

parameters as given

Cs = 10μF, CE = 20μF, Cc = 1μF

Rs = 1KΩ, R1= 40KΩ, R2 = 10KΩ,

RE = 2kΩ, Rc = 4kΩ, RL = 2.2KΩ,

β = 100, r0 = ∞Ω, Vcc = 20V

Cbe = 36 pF, Cbc = 4 pF, Cce = 1 pF, Cwi = 6 pF, Cwo = 8 pF

1. Determine fHi and fHo2. Sketch the high-frequency response using bode plot.

Full frequency response for the BJT amplifier network

• When amplifier stages are cascaded to form a multistage amplifier, the dominant frequency response is determined by the responses of the individual stages. There are two cases to consider:

1. Each stage has a different lower critical frequency and a different upper critical frequency.

2. Each stage has the same lower critical frequency and the same upper critical frequency.

Different critical frequencies• When the lower critical frequency, fL of each amplifier stage is

different, the dominant lower critical frequency f’Lequals the critical frequency of the stage with the highest fL.

• When the upper critical frequency fH, of each amplifier stage is different, the dominant upper critical frequency f’H equals the critical frequency of the stage with the lowest fH.

– Overal Band Width : BW= fH-fL

Multistage Frequency Effects

Equal Critical Frequencies

• When each amplifier stage in a multistage arrangement has equal critical frequencies, the dominant lower critical frequency is increased by a factor of 1:2

• When the upper critical frequencies of each stage are all the same, the dominant upper critical frequency is reduced by a factor of

• * n – is the number of stages in the multistage amplifier.

12'

1

n

LL

ff

Multistage Frequency Effects

121 n

12' 1 nHH ff

Total Frequency Response of a Multistage Amplifier

Once the cutoff frequencies have been determined for each stage (taking into account the shared capacitances), they can be plotted.

Again note the highest Lower Cutoff Frequency (fL) and the lowest Upper Cutoff Frequency (fH)

are closest to the actual response of the amplifier.