Acoustics II: Public Address Systems - ETH Z
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables Acoustics II: public address systems articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back Kurt Heutschi 2019-05-06
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back introduction
PA systems introduction introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I goal of a loudspeaker-based PA system: I generation of sufficiently high sound pressure ( S/N 10.25 dB) in the audience area I homogeneous level distribution ( /- 3 dB) I good direct sound supply I suitable audio quality
PA systems introduction introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I motivation for PA systems: I source is too weak I source is too omnidirectional (strong excitation of diffuse field in a room) I non-acoustical source
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back PA systems for speech
PA systems PA systems for speech introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I PA systems for speech: I auditoria I churches I public buildings (e.g. emergency announcements .)
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back PA systems for speech: speech signals I A-weighted sound pressure level of speech in 1m distance: 65 dB(A) I spectrum:
PA systems PA systems for speech: speech intelligibility introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I relevance of third-octave bands for intelligibility:
PA systems PA systems for speech: necessary frequency range introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I suitably adjusted system frequency response for speech: I attenuation of very low frequencies I attenuation of very high frequencies
PA systems PA systems for speech: elements introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I I I I microphone amplifier loudspeaker room
PA systems PA systems for speech: feed-back problem introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I feed-back loudspeaker microphone: I amplitude response distortions I temporal stretching of transient signals I possible instability (whistling sound) I target: about 10 dB margin to the point of instability
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back maximal amplification
PA systems maximal amplification: system analysis introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I n identical loudspeakers Li I microphone gets direct sound from L1 and diffuse sound from L2 . . . Ln I listener gets direct sound from L1 and diffuse sound from L2 . . . Ln
PA systems maximal amplification: system analysis introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back simplified assumptions: I direct sound: I point source behaviour p I diffuse sound: I constant in the room 1 r -6 dB per doubling of distance
PA systems maximal amplification: block diagram introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back G3 transfer function speaker microphone G2 transfer function microphone signal loudspeaker listener G1 feed-back microphone signal loudspeaker microphone 0.1
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back maximal amplification p2 maximal amplification GMAX p2 E ,withLS E ,withoutLS with G 1 0.1 follows for GMAX GMAX 1 1 2 dQE 0.1 d 21 d 21 n 16π AQ QM LSE 16π A RWLS (γ)RWM (β) d 21 n 16π AQ dQM : distance talker - microphone dLSE : distance loudspeaker - listener dQE : distance talker - listener dLSM : distance loudspeaker - microphone n: number of active loudspeakers A: total absorption Q: loudspeaker directivity (re. full solid angle) RWLS (γ): loudspeaker directivity (attenuation in direction γ) RWM (β): microphone directivity (attenuation in direction β) LSM
PA systems maximal amplification introduction PA speech maximal amplification directional loudspeakers I plausible assumptions in typical applications: I GMAX 1 suppression of feed-back speech intelligibility I reasonable PA system I intelligibility of syllables speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back 2 dLSE n 16π AQ I distance loudspeaker - listener critical distance (considering Q) introduction articulation loss of consonants 1 I n 16π AQ RWLS (γ)RWM (β) d 21 LSM I diffuse field dominates feed-back
PA systems maximal amplification introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I from above can be concluded: I GMAX 1 2 dQM I maximal amplification is inversely proportional to the square of the distance talker - microphone I GMAX 1 n I maximal amplification is inversely proportional to the number of loudspeakers I GMAX Q I maximal amplification is proportional to the loudspeaker directivity
PA systems maximal amplification introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I from above can be concluded: I GMAX 1 2 dQM I maximal amplification is inversely proportional to the square of the distance talker - microphone I GMAX 1 n I maximal amplification is inversely proportional to the number of loudspeakers I GMAX Q I maximal amplification is proportional to the loudspeaker directivity
PA systems maximal amplification introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I from above can be concluded: I GMAX 1 2 dQM I maximal amplification is inversely proportional to the square of the distance talker - microphone I GMAX 1 n I maximal amplification is inversely proportional to the number of loudspeakers I GMAX Q I maximal amplification is proportional to the loudspeaker directivity
PA systems maximal amplification introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I from above can be concluded: I GMAX 1 2 dQM I maximal amplification is inversely proportional to the square of the distance talker - microphone I GMAX 1 n I maximal amplification is inversely proportional to the number of loudspeakers I GMAX Q I maximal amplification is proportional to the loudspeaker directivity
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back maximal amplification: example I auditorium: I V : 2000 m3 I RT : 2 s A: 160 m2 I geometry of the system: I dQM : 0.3 m I dQE dLSE dLSM : 15 m I loudspeaker directivity: I RWLS (γ): 1 I Q: 1 I microphone directivity: I RWM (β): 1 I maximal amplification 6 dB
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back maximal amplification: example I auditorium: I V : 2000 m3 I RT : 2 s A: 160 m2 I geometry of the system: I dQM : 0.3 m I dQE dLSE dLSM : 15 m I loudspeaker directivity: I RWLS (γ): 1 I Q: 1 I microphone directivity: I RWM (β): 1 I maximal amplification 6 dB
PA systems maximal amplification: example introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I maximal amplification 6 dB is not sufficient I to be improved by I microphones with more pronounced directivity I loudspeakers with more pronounced directivity I smaller distance talker - microphone
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back directional loudspeakers
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back horn speakers
PA systems horn speakers introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I properties: I increased efficiency due to improved impedance matching I controlled directivity
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back horn speakers I example mid-range horn, 70x40x40cm:
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back column speakers
PA systems column speakers introduction PA speech maximal amplification directional loudspeakers I arrangement of several chassis in a row I focusing in direction of the row extension suppression of feed-back speech intelligibility introduction example: column of length 1.3 m with 9 chassis: intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back 250 Hz 500 Hz 1 kHz 2 kHz 4 kHz Q 8 11 18 22 18 8 kHz 45
PA systems column speakers introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I reduction of the strong frequency dependency of Q by I segmentation and tilting I individual steering of each chassis
PA systems electronically steered column speakers: line arrays introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I column speakers with I individually steered chassis (delay, frequency response) I control of radiation characteristics in the vertical plane I horizontal directivity defined by chassis characteristics I advantages compared to conventional column speakers: I beam orientation adjustable by electric means vertical mounting possible I radiation characteristics can be optimized (frequency response)
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back electronically steered column speakers: line arrays I sound field of a row of point sources: I I I I 16 chassis 0.5 m separation 500 Hz all chassis in phase
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back electronically steered column speakers: line arrays I sound field of a row of point sources: I I I I 16 chassis 0.5 m separation 500 Hz each chassis with individual delay
PA systems electronically steered column speakers: line arrays introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I radiation characteristics of a row of point sources: I focusing by interference I line source distance dependency with approx. -3dB/distance doubling I limitation to low frequencies: focusing vanishes for array length half of first Fresnel zone I limitation to high frequencies: spacial aliasing for chassis separation wavelength
PA systems line arrays: practical aspects introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I high frequency horns to avoid necessity of many tweeters close to each other I delay adjustment of beam orientation (several simultaneous beams are possible!) I application of frequency filtering (outer chassis radiate low frequencies only) reduction of strong frequency dependency of Q I bending of column at the bottom end for an improved near-field supply (J-form)
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back line arrays: example
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back suppression of feed-back
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back wobbling
PA systems wobbling introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I frequency modulation permanent variation of phase relation in the feed-back path I original idea: 1928 Zwicker: I loudspeaker or microphone suspended on an oscillating pendulum I digital solutions: I optimal modulation frequency: 4.5 Hz I optimal frequency variation: 5 Hz I gain: 5 dB I problem: may become audible at low frequencies
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back notch filter
PA systems notch filter introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I for fixed microphone and loudspeaker positions only a few frequencies dominate possible instability I suppression of these frequencies by narrow band notch filters I typical bandwidth 5 Hz I for moving microphone positions: adaptive filters
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back estimation and compensation of feed-back path
PA systems estimation and compensation of feed-back path introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back example: subtraction filter: I estimation of the feed-back path I simulation of the feed-back path by a digital filter I subtraction of the signal that passed through the feed-back loop once
PA systems estimation and compensation of feed-back path introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back G 1: feed-back path G 10 : estimate of G 1
PA systems estimation and compensation of feed-back path introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I challenge: estimation of feed-back path has to be accurate with respect to phase I systems are time-variant (geometry, air temperature .) I promising strategy: continuous measurement, e.g. with MLS at inaudible level
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back speech intelligibility
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back speech intelligibility: introduction
PA systems speech intelligibility: relevant factors introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I signal/noise ratio I reverberation time I ratio of direct and diffuse sound (determined by total absorption and distance source - receiver) I early reflections (comb filter effects for time of arrival differences of about 1 ms) I late reflections (echoes for time of arrival differences 50 ms)
PA systems speech intelligibility: evaluation introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I subjective measure I percentage of syllables correctly understood intelligibility of syllables I objective descriptors I I I I I Articulation Loss of consonants: ALcons Speech Transmission Index: STI Rapid Speech Transmission Index: RASTI Speech Transmission Index PA: STI-PA Deutlichkeitsgrad: D50
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back intelligibility of syllables
PA systems intelligibility of syllables introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I I I I basis for all measures subjective evaluation with speaker and panel of test persons (listeners) determination of the percentage of correctly understood syllables conversion tables to translate intelligibility of syllables into I intelligibility of words I intelligibility of sentences
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back articulation loss of consonants
PA systems introduction articulation loss of consonants I speech intelligibility parameter for prognosis: PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back 200D 2 RT 2 N V ·Q %ALcons 9RT %ALcons for D 3.2rH for D 3.2rH D: distance source-receiver RT : reverberation time in range 500 Hz. . .2 kHz V : room volume Q: Q factor of loudspeaker WloudspeakerDiffuseFieldContribution N WloudspeakerDirectSoundContribution q QA rH : critical distance 16π A: total absorption
PA systems articulation loss of consonants introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back I with help of %ALcons formula dimensioning of a PA system I significance of %ALcons values: I 10 % very good speech intelligibility I 10. . .15 % good speech intelligibility
PA systems introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization types of PA systems centralized PA systems distributed PA systems summary back speech transmission index
PA systems speech transmission index introduction PA speech maximal amplification directional loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation loss of consonants speech transmission index Deutlichkeitsgrad D50 localization typ
public address systems Kurt Heutschi 2013-01-18. PA systems introduction PA speech maximal ampli cation focusing loudspeakers suppression of feed-back speech intelligibility introduction intelligibility of syllables articulation Loss speech transmission index Deutlichkeitsgrad D50 localization types of PA
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(2) acoustics and architectural programing, (3) acoustics. in school planning, (4) acoustics and facilities design, and (5) acoustics and noise control. The ftlformation is thoroughly illustrated, supported by a. bibliography, and. followed by a checklist for. planners and administrators. (RH)
Sustainable Design and Acoustics The close relationship between acoustics and sustainable design has become increasingly evident in recent years. Taking account of acoustic conditions can greatly increase the overall comfort level of a space, while poor acoustics can re
Chapter 2: Pressure Acoustics Interfaces The Pressure Acoustics, Frequency Domain Interface 52 Domain, Boundary, Edge, Point, and Pair Nodes for the Pressure . Logarithmic and ISO Preferred . . . . . . . 193 Modeling with the Pressure Acoustics Branch (BEM-Based Interface) 194 . 230
