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Progress In Electromagnetics Research, PIER 100, 327–349, 2010

INVESTIGATION INTO TIME- AND FREQUENCY-DOMAIN EMI-INDUCED NOISE IN BISTABLE MULTI-VIBRATOR

H.-C. Tsai

Department of Electronic EngineeringCheng-Shiu UniversityNo. 840, Chengcing Rd., Neausong Township, Kaohsiung CountyTaiwan 83305, R.O.C.

Abstract—Electromagnetic interference (EMI) has a negative effectupon the performance of circuit communication systems. The presentstudy considers the case of EMI induced in a conducting wire, andderives equations to establish the effect of the EMI on a bistablemultivibrator. The validity of the equations is verified experimentally.The results indicate that the degree of influence of the EMI on thebistable oscillator depends on the interference power, the interferencefrequency, the induced power, the output resistance of the circuit,and the parasitic capacitance. Moreover, it is shown that theharmonic noise increases with an increasing interference amplitude andfrequency. The theoretical results are found to be in good agreementwith the experimental data.

1. INTRODUCTION

Since digital circuits can only exist in one of two different discretebinary states, i.e., “on and off” or “high and low”, they are morereliable than their analogue counterparts, whose characteristics andstates are continuous. As a result, digital IC devices are widely usedin many fields throughout engineering and industry. In developingIC circuits, the sensitivity of the device performance to externalfactors such as the component values, component aging, the ambienttemperature, interference signals, EMI and shielding has attractedparticular attention. With the prevalence of Radio Frequency (RF)applications [1, 2] nowadays, such as TVs and radios, amateur radio,

Corresponding author: H.-C. Tsai ([email protected]).

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wireless “walkie-talkies”, cell phones, wireless remote controllers, BlueTooth communication systems [3, 4], and so on, the environmentis rapidly becoming saturated with electromagnetic waves. Someof these electromagnetic waves, termed as “signals”, are useful andnecessary in that they fulfill a specific design purpose. However,others are undesirable since they interfere with the performance ofother electrical or electronic devices. For example, it is well knownthat a cell phone used in close proximity to a computer may cause adistortion of the image on the screen or a static blast from the speakers.Similarly, cell phones may disrupt the delicate flight instrumentationonboard an aircraft and are therefore banned in flight. Finally, in acommunications/broadcasting context, interference may be manifestedin the form of “cross talk”, a phenomenon in which the conversationsof others are detected when speaking over the cell phone, or mayresult in the reception of two different radio stations at the samefrequency. Whilst in some cases, the effects of EMI are no morethan a minor irritant (e.g., the screen distortion caused by the useof a wireless emitting device near a TV), in others, they may bepotentially lethal (e.g., the use of a cell phone onboard an aircraft). Asa result, it is essential that the effects of EMI on common electroniccomponents are thoroughly understood [5–19]. Accordingly, thepresent study considers the EMI response of a bistable multivibrator,a component with wide-ranging applications in the electronics field,including Ref. [20–22]. In a normal indoor environment, the intensityof the low frequency electromagnetic waves is greater than that ofthe high frequency waves, i.e., 0.03µT and 0.0067µT, respectively(as measured by the current authors using CA40/43 instrumentation(Chauvin Arnoux, France)). Therefore, in analyzing the effects of EMIon the bistable multivibrator, the present analyses focus specifically onthe effects of low frequency EMI.

2. EXPERIMENTAL SETUP

Figure 1 illustrates the experimental setup used in this study tomeasure the interference noise spectrum induced in the bistablemultivibrator. The arrangement has the advantage that both theamplitude and the frequency of the EMI noise can be easily controlled.As shown, the experimental system was shielded within a metal caseto suppress the effects of external noise, and the amplifier and currentsource were both battery operated. In the experiments, EMI witha frequency ranging from 200 ∼ 900Hz and an amplitude between0.2V and 0.9V was induced in a conducting wire (CW) positioned inthe air gap of a ferromagnetic toroid wrapped with a current-carrying

Progress In Electromagnetics Research, PIER 100, 2010 329

Bistable

circuit

A

B

Shielding

Low NoiseAmplifier

Personal

Computer

Printer

Oscilloscope or Signal Analyzer

R

CW

C C

RS

L

Figure 1. Experimental setup for noise measurement in bistablemultivibrator.

coil, where CW is a circular wire with aluminum alloy material, thediameter is 0.001 m. The EMI interference was detected initially asradiated noise, amplified by a 73.98 dB low-noise pre-amplifier suchthat it could be detected using an oscilloscope, and then coupled inseries with the bistable multivibrator in the form of conducted noise.The EMI signals were transmitted to the oscilloscope via a circuitcoupling and were then passed to a spectrum analyzer (model HPE4440A) controlled by a PC via an IEEE-488 bus in order to obtain thetime domain and frequency spectrum plots of the interference signals.

3. THEORETICAL ANALYSIS

Multivibrators are two-state, digital circuits which employ positivefeed-back during state changes. Three different classes of multivibratorexist, namely bistable, monostable, and astable. The bistablemultivibrator, also known as a flip-flop, latch or binary circuit,is characterized by two stable states, which persist indefinitelyunless deliberately changed. Of all the multivibrators, the bistablemultivibrator is one of the most commonly used (typically forapplications such as single bit information storage), and is thereforechosen for analysis purposes in the present study.

3.1. Basic Parameters of Bistable Multivibrator

Figure 2 presents the basic circuit of a bistable multivibrator. Let thelogical output state of the multivibrator be denoted as Q. When Q = 1,the inverter has a complementary logical output, i.e., Q=0. This state

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: Interfered point

RC1R2R1

V CC

RC2

C2C1

Q2Q1

V OUT

R5 R6

D1 D2

C3 C4R3 R4

D3 D4V IN

C C

RL

Figure 2. Bistable multivibrator circuit.

persists until an excitation signal is applied, at which point it flip-flopsto the complementary value. This new state is then maintained untila further excitation signal is applied, and so on. As shown in Fig. 2,the multivibrator circuit is symmetrical, i.e., RC1 = RC2, C1 = C2,R1 = R2, R3 = R4, R5 = R6, and C3 = C4, Q1 and Q2 are thesame type, but which is impossible to have the same characteristics.Furthermore, transistors Q1 and Q2 are of same type, but have differentcharacteristics such that when one is “on”, the other is “off”.

3.1.1. Circuit Design

Assume that when the power is initially turned on, Q1 is “on” and Q2

is “off”. Assume also that VCE1(sat) = 0.2V and RC1 = RC2 = 1K .From the circuit, it can be shown that

IC1(sat) =VCC − 0.2V

RC1=

1.4− 0.21K

= 1.2mA (1)

Check

βIB1 > IC1(sat) (2)

IB1(sat·min) ≥IC1(sat)

β=

1.2mA157

= 7.64µA (3)

Select VCE2(off ) = 1.05V

IC2(off ) =VCC − VCE2(off )

RC2=

1.4− 1.051K

= 0.35mA (4)


Obtain

R2 =VCE2(off ) − VBE1(sat)

IC2(off )=

1.05V − 0.7V

0.35mA= 1K (5)

Select R5 = 2.2K

IR5 =VBE1

R5=

0.72.2K

= 0.318 mA (6)

Obtain

IB1 = IC2(off ) − IR5 = 0.35 mA− 0.318mA= 32 µA > IB1(sat·min) = 7.64µA (7)

From Kirchhoff’s voltage law, it follows that

RC1 ¿ R1 + R6, RC2 ¿ R2 + R5 (8)

SelectVCE2(off ) = 1.05V ,

ImpliesVRC2 = 1.4V − 1.05V = 0.35V

Check

VRC2 = 1.4V 1K

1K + 1K + 2.2K= 0.33V ∼= 0.35V

Differential Circuit:Select

R3 = 12RC1 = 12K = R4, f = 20K , T = 50µs,

TakeC3 = C4 = 0.001µf

3.2. Electromagnetic Interference

In the present study, the interference source has the form of a current-carrying coil wound on a ferromagnetic toroid with an air gap. Whena current is passed through the coil, an EMI voltage of magnitude Veff

is induced in a conducting wire (CW) positioned within the air gap.The magnetic field density and flux density in the air gap are givenrespectively by [23]

Hg =µNI0

µ0 (2πr0 − lg) + µlg(9)

PrB =12

∫µ0H

2g dv =

12

∫HgBgdv (10)

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where µ0 is the permeability of free space, µ is the permeability of theferromagnetic material, I0 is the current within the coil, r0 is the meanradius of the toroid, and lg is the width of the air gap. The value ofPrB represents the average energy per second of the interference on theCW, and can be calculated from Eq. (10) or measured directly.

In general, any periodic signal can be represented by the followingcomplex Fourier series:

V (t) =∞∑

n=−∞Cnejnωt = C0 +

∞∑

n=1

2 |Cn| cos (nωt + ∠Cn) (11)

where

Cn =1T

∫ T2

−T2

V (t) ejnωtdt (12)

In the present experiments, the input signal of the ferromagnetic toroidhas the form of a periodic square wave, as shown in Fig. 3. In this case,the following Fourier transform applies:

Cn =1T

∫ t0

0V0 (t) e−jnωtdt =

V0t0T

sin 12nωt0

12nωt0

e−j 12nωt0 (13)

and

Kn =V0t0T

sin 12nωt0

12nωt0

(14)

∠Cn =12nωt0 (15)

Substituting Eqs. (14) and (15) into Eq. (11) gives

V (t) =V0

2+

∞∑

n=1

Kn cos(nωt0 +

nπ

2

), for t0 =

T

2(16)

Figure 4 shows the equivalent circuit of the ferromagnetic toroid.The following admittance can be obtained:

Y =(Rω + jnωL) + 1

jnωCω

(Rω + jnωL) 1jnωCω

=1

R2ω+n2ω2L2

[Rω+j

(nωR2

ωCω−nωL+n3ω3L2Cω

)]=|Y |∠θ1 (17)

I (jnω) = Y V (t) = C0Y0 +∞∑

n=1

2Kn |Y | cos (nωt + ∠Cn + θ1) (18)


From Eq. (9), it can be shown that

Veff = − 1dt

∫

s

~B · d~s = − 1dt

[µ0µNI (jnω)

µ0 (2πr0 − lg) + µlg·∆zd

]

=µ0µN (∆zd)

µ0 (2πr0 − lg) + µlg

∞∑

n=1

2Kn |Y |nω sin (nωt + ∠Cn + θ1)

=∞∑

n=1

2KKn |Y |nω sin (nωt + ∠Cn + θ1) (19)

K =µ0µN∆zd

µ0 (2πr0 − lg) + µlg(20)

Figure 5 shows the equivalent circuit of the experimental measurementsystem.

The Vout signal supplied to the oscilloscope and signal analyzer isgiven by

Vout = VeffK1

RS· K3∠θ3

K2∠θ2· Ri

K4∠θ4(21)

Tt0

Vi (t)

t

V0

Figure 3. Experimental inputsignal of ferromagnetic toroid.

i C

L Rω

ω

Figure 4. Equivalent circuit offerromagnetic toroid.

C CRS

Signal

Analyzer

Cce

Rm RLV eff

Figure 5. Equivalent circuit of experimental measurement system.

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where K1 = RS//Rm, Rm = 1/hoe//Rc2//R2//R4 for a small valueof Cce.

Q2 = K1 − j1

ωC= K2∠θ2 (22)

K2 =

[K2

1 +(

1ωC

)2] 1

2

θ2 = tan−1 − 1ωC

K1(23)

Q3 = K2∠θ2//RL = K3∠θ3 = a + bj (24)

K3 =1

(K1 + R2)2 +

(1

ωC

)2

[K1RL(K1+RL)+

R2

ω2C2

]2

+[K1RL

ωC−(K1+RL)

RL

ωC

]21/2

θ3 = tan−1K1RL

ωC − (K1 + RL) RLωC

K1RL (K1 + RL) + RLω2C2

(25)

Q4 = (RS//Rm + XC) //RL + XC + Ri = Q3 + XC + Ri

= a + Ri + j

(b− 1

ωC

)= K4∠θ4 (26)

K4 =

[(a + Ri)

2 +(

b− 1ωC

)2] 1

2

(27)

θ4 = tan−1 b− 1ωC

a + Ri(28)

From the above, it can be shown that

Vout =∞∑

n=1

2KKn |Y |nωK1K3Risin(nωt+∠Cn+θ1+θ3−θ2−θ4)RsK2K4

Vout =∞∑

n=1

C32KKn |Y |nωK1K3Ri

RsK2K4sin(nωt+∠Cn+θ1+θ3−θ2−θ4)

(29)

where the constant C3 is the effective inducted coefficient. Eq. (29)shows that the magnitude of the EMI-induced noise is governed bythe pulse height, the output load, the parasitic capacitance, theinterference frequency and the interference amplitude.

3.3. Noise Analysis

Conducting wires render IC circuits highly susceptible to the effectsof electromagnetic interference and noise [24–29]. When a periodic


square wave is applied across points A and B in Fig. 1, the CW inthe air gap of the ferromagnetic torroid induces a pulse voltage inthe bistable multivibrator circuit, which in turn produces a responsenoise spectrum. Fig. 6 shows the typical response wave for a periodicpulse with a period T . The periodic pulse function can be analyzed bytaking the discrete Fourier transformation of function Sn, where Sn isa function of A1 and A2 (i.e., the pulse heights), i.e.,

Sn =1T

0∫

−T0

−A1e−a(T0+t)e−jωntdt +

T0∫

0

A2e−ate−jωntdt

=1T

a− jωn

a2 + ω2n2[E − jD] (30)

whereE = A1e

−aT0 + A2 −A2e−aT0 cosωnT0 −A1 cosωnT0 (31)

D = −A2e−aT0 sinωnT0 + A1 sinωnT0 (32)

S2n =

1T 2(a2 + ω2n2)

[E2 + D2

](33)

in which n is an integer, ω = 2πf = 2π/T , a is the attenuation factorof the exponential function, and A1 and A2 are the amplitudes of theupper-half and lower-half periods of the EMI induced by the CW,respectively.

0.000 0.001 0.002

-600.0 m

-400.0 m

-200.0 m

0.0

200.0 m

400.0 m

600.0 m

Vol

tage

(V

)

Time (Second)

Measurement

Simulation

Figure 6. Experimental and simulation results for typical periodicpulse wave generated by periodic EMI signal with period T .

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s

eff

R

VCce Ro= Rs //Rm //R i

Figure 7. Simplified representation of EMI output port in Fig. 1.

The amplitude spectrum of the EMI current can be obtained byplotting Sn against discrete frequencies, i.e., ωn. The square of Sn hasdimensions A2 and corresponds to the current power spectrum Siλ(fn)over 2T [30].

Figure 7 shows the Norton equivalent output circuit of the bistablemultivibrator, where Cce is the parasitic capacitance between the drainand the source. Let Vce = VC and Cce = C, then

in = iC + i0 = Cd∆VC

dt+

∆VC

R0⇒ d∆VC

dt+

∆VC

R0C=

inC

(34)

where R0 = Rs//Rm//Ri, and ∆Vc is the variation in the voltageacross the capacitor.

Taking the Fourier series expansions of ∆Vc and iλ gives

inC

=1C

∞∑n=−∞

αn exp(jωnt) (35)

d(∆Vcn)dt

+∆Vcn

R0C=

1C

αn exp(jωnt) (36)

From which it can be shown that

∆Vcn = βn exp(jωnt) (37)

whereβn =

αnR0

1 + jωnR0C(38)

Therefore, the noise power spectrum, S∆V c(fn), of the bistablemultivibrator induced by the EMI is given by

S∆V c(fn) = 2Tβnβ∗n (39)

S∆V c(fn) = Siλ(fn)R2

0

1 + (ω1nR0C)2(40)

whereSiλ(fn) = 2Tαnα∗n = 2TS2

n (41)


RC2

RO2

VBM

RS

RO1

Veff

(a) (b)

Figure 8. Output equivalent circuits of (a) EMI signal and (b) bistablemultibibrator signal.

From Eqs. (5), (12) and (13), it can be shown that

S∆VC(fn) = 2T

R20

1 + (ω1nR0C)2

[1

T 2(a2 + ω2n2)(E2 + D2)

](42)

The total noise power induced in the bistable multivibratorcan be obtained by summing S∆V c(fn) over all possible integers,n. In identifying the relative magnitudes of the various harmoniccomponents within the power spectrum, the present analysis firstfinds the value of A (the pulse height) from the measured powerspectral intensity of the fundamental harmonic and then evaluates thepower spectral intensities of the higher-order harmonics. Adopting thisapproach, the typical experimental response wave shown in Fig. 6 canbe transformed into the noise spectrum shown in Fig. 9 and the valueof the EMI then quantified directly.

3.4. Effects of Basic Bistable Multivibrator Frequency onOutput Power

The basic output frequency of a bistable multivibrator has the formof a square wave. Generally speaking, the effects of the basic outputfrequency on the noise power spectrum of the multivibrator can bemitigated using an impedance-matching method. Fig. 8(a) shows theoutput equivalent circuit of the EMI signal supplied to the oscilloscopeor signal analyzer, where RO1 = 1/hoe//RC2//R2//R4//RL//Ri =45.21Ω. Meanwhile, Fig. 8(b) shows the equivalent circuit of thebistable multivibrator square wave output signal, where RO2 =1/hoe//RS//R2//R4//RL//Ri = 24.31Ω. The output powers of the

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EMI and multivibrator signals can be obtained respectively as

PEMI =(

Veff

50 + 45.21

)2

45.21 = 0.005(Veff )2 (43)

PBM =(

VBM

1k + 24.31

)2

24.31 = 2.32× 10−5(VBM )2 (44)

Here, PBM/PEMI = 0.0046. In other words, the output power ofthe bistable multivibrator is negligible compared to that of the EMIinduced signal and can therefore be neglected.

4. RESULTS AND DISCUSSION

Figure 6 presents the experimental and simulation results for thetypical periodic pulse function generated by a periodic EMI signalwith a period T . Note that in obtaining the simulation results usingEq. (29), the following parameter settings are assumed: V0 = 0.56V(at time t = 0), V0 = 0.45V (at time t = T/2), µ0 = 4πE − 7H/m,µr = 4000, N = 500, F = 500 Hz, Rω = 0.52Ω, r0 = 0.09m,lg = 0.005 m, Cω = 6.558E − 10F, 1/hoe = 30 kΩ, Rc1 = Rc2 = 1 kΩ,R1 = R2 = 1kΩ, R3 = R4 = 12 kΩ, C = 100E − 6F, ∆z = 0.01m,d = 0.001 m, Rs = 50 Ω, C3 = 0.081, XC = 1/(2πfC), RL = 220 kΩ,L = 1E − 4H, ω = 2πf and Ri = 50 Ω. Fig. 6 confirms that agood agreement exists between the simulated pulse function and theexperimental function. In the experimental setup shown in Fig. 1,Cce = 12.77E − 8F, RL = 220 kΩ, and T0 = 0.4990T . Utilizing avalue of a = 13622 in Eq. (42), Fig. 9 compares the experimentaland simulation results for the harmonic wave component of the noisespectrum induced in the bistable multivibrator by EMI with anamplitude of VP = 0.4V and a frequency of f = 500Hz. Again, agood agreement is observed between the two sets of results. To furtherinvestigate the effect of EMI on the noise spectrum induced in thebistable multivibrator, the amplitude of the AC interference signal wasvaried between 0.2 V and 0.9 V while the frequency was maintained at aconstant f = 500 Hz. Fig. 10 presents the corresponding experimentaland simulation results for the odd-order harmonics of the inducednoise spectrum. Note that in obtaining the simulation results usingEq. (42), A1 ranges from 5364 ∼ 33006µA while A2 ranges from 5514∼ 33930µA. It is observed that a good agreement is obtained betweenthe experimental and simulation results at all values of Vp.

Table 1 compares the measured and simulated peak values of theharmonic components of the maximum noise power spectral intensityfor EMI with amplitudes in the range VP = 0.2 ∼ 0.9V and a constant


0 2000 4000 6000 8000 10000

-80

-60

-40

-20

0

20

40

SVc

(fn )

(DB

mA

/Hz^

1/2)

Frequency (Hz)

:Measurement :Simulation

Figure 9. Harmonic wave component of bistable multivibrator noisespectrum response for VP = 0.4V and f = 500 Hz. (Note that inobtaining simulation results using Eq. (42), A1 and A2 are specified as12208µA and 12549µA, respectively.)

0 2000 4000 6000 8000 100000

10

20

30

40

50

SVc

(fn)

(DB

mA

/Hz^

1/2)

Frequency(Hz)

All f=500 Hz1.Vp=0.9 V Measurement

Simulation2.Vp=0.8 V Measurement







Simulation

Figure 10. Experimental and simulation results for odd-orderharmonics of noise spectrum induced by EMI interference withfrequency of 500 Hz and amplitude of Vp = 0.2 ∼ 0.9V. (Simulationresults computed using Eq. (42) shown using filled symbols).

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0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

10

20

30

40

SVc

(fn )(

DB

mA

/Hz^

1/2)

Frequency(Hz)

All Vp=1 V

1.F=700 Hz Measurement Simulation





Figure 11. Experimental and simulation results for odd-orderharmonics of noise spectrum induced by EMI interference frequency of300 ∼ 700Hz and amplitude of Vp = 1 V. (Simulation results computedusing Eq. (42) shown using filled symbols.)

0 1000 2000 3000 4000 5000 6000 7000 8000 9000 100000

10

20

30

40

SVc

(fn )(

DB

mA

/Hz^

1/2)

Frequency(Hz)

All Vp=1 V






Figure 12. Experimental and simulation results for odd-orderharmonics of noise spectrum induced by EMI interference frequencyof 300 ∼ 700Hz and variable amplitude parameters A1 and A2 (seeTable 3). (Simulation results computed using Eq. (42) shown usingfilled symbols.)


Table 1. Comparison of experimental and theoretical results formaximum noise power spectral intensity for various values of Vp.

Frequency fixed, Amplitude variable (First harmonic wave)

Vp (V) 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Frequency

(Hz)500 500 500 500 500 500 500 500

Measurement

(dBmA/Hz1/2)21.1 24.6 28 30.2 32.1 33.8 35.3 36.6

Simulation

(dBmA/Hz1/2)20.90 24.6 28.07 30.18 32.15 33.82 35.47 36.71

Table 2. Comparison of experimental and theoretical results formaximum noise power spectral intensity for various values of frequency.

Amplitude fixed, Frequency variable (First harmonic wave)

Frequency (Hz) 200 300 400 500 600 700 800 900

Measurement

(dBmA/Hz1/2)25.6 27.7 29.1 30.2 31 31.8 32.3 32.7

Simulation

(dBmA/Hz1/2)26.39 28.1 29.29 30.18 30.87 31.43 31.89 32.27

frequency of f = 500Hz, i.e., the harmonic value varies only as afunction of the interference amplitude while the remaining parametersare constant. Table 2 compares the experimental and simulation resultsfor the maximum noise power spectral intensity for EMI frequenciesin the range 200 ∼ 900Hz and a constant interference amplitude ofA1 = 15565µA and A2 = 16001µA, i.e., the noise power spectralintensity varies only as a function of the AC interference frequencywhile the other parameters remain constant. Fig. 11 presents theexperimental and simulation results for the odd-order harmonics ofthe noise spectrum induced by EMI interference with a frequencyof 300 ∼ 700Hz and an amplitude of Vp = 1 V. Although a −2 dBdifference is observed between the two sets of results, it is clear thatthe EMI frequency has a significant effect upon the noise response ofthe multivibrator. By tuning the amplitude parameters in recognitionof the fact that a variable EMI frequency affects both the attenuationfactor and the induced wave type, the same degree of simulationaccuracy as that shown in Fig. 10 can be obtained, as shown inFig. 12 and Table 3. In other words, the EMI frequency is a function

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of the EMI amplitude, as proven in Eqs. (29) and (42). AlthoughFig. 11 shows that the frequency has a significant effect on theodd-order harmonic waves, i.e., Eq. (42) denotes dω/dA1 6= 0 anddω/dA2 6= 0 for the nonlinear function S∆V c(fn), Fig. 9 shows thatthe difference between the experimental and simulation results for thevariable amplitude case is less than that for the variable frequency case.In other words, the amplitude of the EMI has a greater effect on thenoise response of the bistable multivibrator than the EMI frequency.In practice, this finding implies that the parasitic capacitance andthe dynamic input resistance of the multivibrator vary with a varyingfrequency.

Table 3. Comparison of experimental and theoretical results formaximum noise power spectral intensity for various values of frequencyand amplitude.

Amplitude, Frequency variable (First harmonic wave)Frequency (Hz) 300 400 500 600 700

InducedCurrentA1 (µA)

13165 14065 15565 16065 16865

InducedCurrentA2 (µA)

13533 14459 16001 16515 17337

Measurement(dBmA/Hz1/2)

27.7 29.1 30.2 31 31.8

Simulation(dBmA/Hz1/2)

26.65 28.41 30.18 31.24 32.13

Table 4. Comparison the simulations for various values of frequency,amplitude and attenuation factor with Vp = 0.2V, f = 500 Hz.

Parameters a A1 (µA) A2 (µA)Remarks

(Shown in)Curve a. 13622 5364 5514 Figs. 10, 13Curve b. 11376 4624 4753 Fig. 13Curve c. 8622 3642 3742 Fig. 13


Table 5. Relative SNR of current induced by EMI.

VP (V) 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2

Induced

Current

A1 (µA)

33006 28643 23661 19534 15565 12208 8193 5364

Induced

Current

A2 (µA)

33930 29445 24323 20081 16001 12549 8422 5514

Induced

Peak

Current

Ni (µA)

6.6936 5.8088 4.7984 3.9615 3.1566 2.4757 1.6615 1.0878

Relative

SNR

(dBµA)

3.487∗ 4.718∗ 6.378∗ 8.043∗ 10.016∗ 12.126∗ 15.590∗ 19.269∗

*where SNR = 20 log(Si/Ni), Si = 10 µA,

Ni = ((A1 + A2)/2)/5000 and f = 500Hz.

If we want to probe the more accuracy of Fig. 10, the attenuationfactor a must be considered as a variable of power spectral intensityfunction. We take a curve of VP = 0.2V in Fig. 10 to illustrate theresult. Table 4 shows the noise power spectral intensity varies as afunction of the AC interference frequency, amplitude and attenuationfactor a, we can find that the simulation of curve b and c in Fig. 13reveal the more accuracy than curve a. In general, the simulation andexperimental results presented above indicate that the magnitude ofthe EMI induced by the CW is affected by the amplitude, frequencyand period of the interference signal, the drain resistance and parasiticcapacitance of the multivibrator, the output load, and parametera. Table 5 indicates the relative signal-to-noise (SNR) ratio of themultivibrator for interference amplitudes in the range VP = 0.2 ∼0.9V, a constant frequency of f = 500Hz and a reference signalSi of 10µA. The CW used in the present EMI experiments has alength of 1 cm. Thus, if the CW in a practical electrical circuit hasa length of 1 m (say), the EMI effects will potentially be magnified 100times compared to that observed in the present study. For example,assuming an induced current of 3.157µA, a CW of length 1 cm, anda load resistance of 45 Ω, the induced voltage is 142µV. This valuemay then be amplified by up to 1000 times in a practical system, andthus a significant EMI effect occurs. According to CISPR 11 (The

344 Tsai

International Special Committee on Radio Interference), EMI shouldbe limited to no more than 110 dBµV in the interference frequencyrange 0.009 ∼ 0.050MHz, equivalent to a voltage of 316227µV. As aresult, a useful design guideline of 2.226 cm for the maximum lengthof the CW in bistable multivibrator circuits can be inferred. Thebasic theorem presented in this paper is applicable to different circuits.However, the actual derived formulae are specific to the particularcircuit. If the EMI perturbs the Wien bridge oscillator (WBO) asFig. 14, the same results as those obtained in the present discussions.Fig. 15 compares the experimental and simulation results obtainedfor the harmonic components in the noise spectrum of a WBO forVP = 0.3V ∼ 1.0V. Comparing these results with those presented inFig. 10 for the bistable multivibrator, it can be seen that the resultsare broadly similar. However, the function level is somewhat higherdue to the different parameters of the two circuits.

The preceding discussions have considered the effects of lowfrequency interference. However, as shown in the following, the basictheorems developed in this study can also be applied to the case ofhigh frequency interference. Fig. 16 shows that a good agreement isobtained between the experimental results and the simulation resultsfor the noise spectrum responses induced by EMI with a frequency of500 kHz with Vp = 0.4 ∼ 1.6 V of MOSFET circuit.

0 2000 4000 6000 8000 100000

10

20

30

40

50

SV

c (f

n)(

DB

mA

/Hz^1

/2)

Frequency(Hz)

All f=500Hz

1.Vp=0.2V Measurement

a. Simulation

b. Simulation

c. Simulation

Figure 13. The noise power spectral intensity varies as a function ofthe AC interference frequency, amplitude and the attenuation factor awith Table 4 data.


+

R

C

C=0.01

R=1K

R2=10K

Y

R1=1K

X

+ 10 f

RB1

=1M

RC1

=5K

+

RE1

=1K

D

RB2

=1M

RC2

=5K

+

VCC=10V

RE2

=1K

+

Oscilloscope

or Signal

Analyzer

C C

RL2

D is the interfered

point of EMI signal

− − −

−

µ

10 f µ10 f µ

µ

10 f µ

Figure 14. The circuit of WBO.

0 2000 4000 6000 8000 10000 12000 140000

10

20

30

40

50

SV

c (f

n)(

dB

mA

/Hz^1

/2)

Frequency(Hz)

All f=500Hz


Simulation


Simulation


Simulation


Simulation


Simulation


Simulation


Simulation


Simulation

Figure 15. Experimental and simulated results for odd-orderharmonics at 500Hz with Vp = 0.3V to 1.0V of WBO.

346 Tsai

0 1000000 2000000 3000000 4000000 5000000-50

-40

-30

-20

-10

0

10

S?

Vc (f

n)(

DB

mA

)

Frequency(Hz)

All f=500 kHz


Simulation


Simulation


Simulation


Simulation


Simulation


Simulation


Simulation

Figure 16. Experimental and simulated results at 500 kHz withVp = 0.4V to 1.6 V of MOSFET circuit.

5. CONCLUSIONS

Experimental and theoretical methods have been used to characterizethe noise spectrum of a bistable multivibrator subject to periodic EMIinduced via a CW. A good agreement has been observed between theexperimental and simulation results for the noise spectral intensity ofthe bistable multivibrator in both the time domain and the frequencydomain. In general, the results have shown that the noise responseof the multivibrator is significantly affected by EMI. Specifically, thedegree of the EMI effect on the bistable oscillator is determined bythe radiated power and the following circuit parameters: f , V0, µ0,µr, N , Rω, r0, lg, Rs, Rc1, Rc2, R1, R2, R3, R4, Cω, Cce, Ri, ∆z,d, L, A1, A2, a, T0, RL and C. Furthermore, it has been shownthat the magnitude of the induced interference current increases withan increasing interference frequency and an increasing interferenceamplitude. Of these two characteristics, the amplitude has a greatereffect on the noise response of the multivibrator than the frequency.However, a variable EMI frequency influences both the attenuationfactor and the induced wave type. In accordance with CISPR andEN norms, the results presented in this study imply that the CWsused in practical bistable multivibrator circuits should not exceed alength of 2.226 cm. Whilst the methods outlined in this study havefocused specifically on the case of bistable multivibrators, they areequally applicable to the EMI analysis of all general wavelength-basedelectronic devices.


ACKNOWLEDGMENT

The author wishes to acknowledge the invaluable assistance providedby Haw-Jiun Liang in the course of this study.

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